Enhanced hybrid systems and methods for characterizing stress in chemically strengthened transparent substrates

ABSTRACT

The hybrid measurement system includes an evanescent prism coupling spectroscopy (EPCS) sub-system and a light-scattering polarimetry (LSP) sub-system. The EPCS sub-system includes an EPCS light source system optically coupled to an EPCS detector system through an EPCS coupling prism. The LSP sub-system includes an LSP light source optically coupled to an optical compensator, which in turn is optically coupled to a LSP detector system via a LSP coupling prism. A support structure supports the EPCS and LSP coupling prisms to define a coupling prism assembly, which supports the two prisms at a measurement location. Stress measurements made using the EPCS and LSP sub-systems are combined to fully characterize the stress properties of a transparent chemically strengthened substrate. Methods of processing the EPCS and LSP measurements and enhanced configurations of the EPCS and LPS sub-systems to improve measurement accuracy are also disclosed.

This application claims the benefit of priority of U.S. ProvisionalApplication Ser. No. 63/152,021 filed on Feb. 22, 2021 the content ofwhich is relied upon and incorporated herein by reference in itsentirety.

FIELD

The present disclosure relates to characterizing stress in transparentchemically strengthened substrates, and in particular relates toenhanced hybrid systems and methods for characterizing stress chemicallystrengthened transparent substrates.

BACKGROUND

Transparent substrates that have undergone a chemical strengtheningprocess exhibit increased resistance to scratching and breaking. Suchsubstrates extremely useful for a variety of display applicationsranging from television screens to computer screens to mobile hand-helddevice screens to watches. An example chemical strengthening process isan ion-exchange (IOX) process, whereby ions in a near-surface region ofa glass-based substrate are exchanged for external ions, e.g., from asalt bath.

Manufacturing transparent chemically strengthened (CS) substratesrequires characterizing their stress characteristics to ensure the CSsubstrates have the desired levels of chemical strengthening suitablefor the given application. The characterization typically requiresmeasuring a stress profile of the CS substrate from the surface to thecenter, along with related stress parameters, such as the surfacecompressive stress, the knee stress, the spike depth of layer, the totaldepth of layer, the depth of compression and the central tension. Otherstress-related parameters include the variation in the birefringencewith depth into the CS substrate.

There are two main methods used to characterize stress of a transparentCS substrate. The first utilizes evanescent prism coupling spectroscopy(EPCS). The EPCS method using a coupling prism to couple light intoguided modes supported by a near-surface waveguide (NSWG) formed in thesubstrate, e.g., by an IOX process. A coupling prism is also used tocouple light out of the NSWG to form a guided mode spectrum. The guidemode spectrum includes a transverse electric (TE) mode spectrum with TEmode lines and a transverse magnetic (TM) spectrum with TM mode lines.The TE and TM modes lines are analyzed to extract stress-relatedcharacteristics, including a stress profile. The EPCS method isparticularly useful for characterizing stress in the near-surface regionof the CS substrate (e.g., surface compressive stress and spike depth oflayer) but is not useful for characterizing a central tension CT anddepth of compression DOC that reside deeper within the substrate.

The second main method utilizes light-scattering polarimetry (LSP). InLSP, the CS substrate is irradiated with input laser light at arelatively shallow angle through a coupling prism. The laser lightpolarization is varied continuously between different polarizationstates using an optical compensator. The scattered light is detected byan image sensor. Stress in the CS substrate causes optical retardationalong the light path, with the amount of stress being proportional tothe derivative of the optical retardation. The amount of opticalretardation can be determined from the detected scattered lightintensity distribution, which varies due to the constructive anddestructive interference for the different effective path lengths of thedetected light. The LSP method is useful for measuring certainstress-related properties, such as the central tension (CT) and depth ofcompression (DOC) but is not useful for measuring near-surfacestress-related properties.

Presently, to fully characterize the stress profile of a CS substratefrom the surface to the center, the CS substrate is first measured usinga EPCS measurement system and is them moved to a LSP measurement systemand the two measurement stitched together. This is time consuming andintroduces the risk of breakage by having to handle the CS substratewhen moving the CS substrate between the two measurement systems.

It would therefore be more advantageous to have a single measurementsystem capable of performing enhanced EPCS and LSP measurements.

SUMMARY

The hybrid measurement systems and methods disclosed herein enable afull stress characterization of a transparent CS substrate, includingthe surface stress S(0), the near-surface compressive stress profileS(x) including the knee stress S_(k)=S(x_(k)), the depth of layer DOL,the central tension CT, and the depth of compression DOC. The fullstress characterization is obtained by combining the stress calculationsusing both EPCS and LSP measurements.

An embodiment of the disclosure is directed to a system forcharacterizing stress in a CS substrate having a top surface and anear-surface waveguide. The system comprises: an EPCS sub-systemcomprising a EPCS light source system and a EPCS detector system inoptical communication through an EPCS coupling prism having a EPCScoupling surface; a LSP sub-system comprising a LSP light source system,an optical compensator and a LSP detector system in opticalcommunication with the optical compensator through an LSP coupling prismhaving a LSP coupling surface; a coupling prism assembly comprising aprism support frame configured to operably support the EPCS and LSPcoupling prisms so that the EPCS and LSP coupling surfaces residessubstantially in a common plane; and a support plenum having a surfaceand a measurement aperture, the support plenum configured to support theCS substrate at a measurement plane at the measurement aperture, and tooperably support the coupling prism assembly at the measurement apertureso that the EPCS and LSP coupling surfaces reside substantially at themeasurement plane. In an example, the EPC sub-system and/or the LSPsub-system have the enhanced configurations as described below.

Another embodiment of the disclosure is directed to a method ofmeasuring first and second stress characteristics of a CS substratehaving a surface and a near-surface waveguide, comprising: operablydisposing the surface of the CS substrate relative to a coupling prismassembly at a measurement location, the coupling prism assemblycomprising an EPCS coupling prism and a LSP coupling prism torespectively define adjacent EPCS and LSP coupling interfaces;performing a EPCS measurement of the CS substrate using the EPCScoupling interface to obtain the first stress characteristics andperforming a LSP measurement of the CS substrate using the LSP couplinginterface to obtain the second stress characteristics without removingeither the coupling prism assembly or the CS substrate from themeasurement location; and combining the first and second stresscharacteristics to establish a full stress characterization of the CSsubstrate. In an example, the EPC sub-system and/or the LSP sub-systemshaving the enhanced configurations as described below can be used tocarry out enhanced methods of measuring the first and second stresscharacteristics.

Another embodiment of the disclosure is directed to an EPCS system forcharacterizing stress in a CS substrate having a surface and anear-surface waveguide, comprising:

a) an EPCS light source system comprising:

-   -   i) an EPCS light source that emits a multiwavelength EPCS light        beam;    -   ii) an optical filter assembly configured to sequentially filter        the multiwavelength EPCS light beam to form a sequence of        filtered EPCS light beams having different wavelengths;    -   iii) a light guide assembly that transfers the sequence of        filtered EPCS light beams as guided light to a focusing optical        system arranged to receive the transferred filtered EPCS light        beams and form therefrom a sequence of filtered and focused EPCS        light beams;

b) an EPCS coupling prism that forms an EPCS coupling surface with thesurface of the CS substrate and that receives and couples the sequenceof filtered and focused EPCS light beams into and out of thenear-surface waveguide at the EPCS coupling surface to form a sequenceof filtered and reflected EPCS light beams that respectively comprisemode spectra of the near-surface waveguide for the correspondingfiltered and reflected EPCS light beam; and

c) an EPCS detector system comprising:

-   -   i) a switchable polarization filter operably connected to a        polarization controller to sequentially perform transverse        magnetic (TM) and transverse electric (TE) polarization        filtering of the sequence of filtered and reflected EPCS light        beams to form TM and TE filtered and reflected EPCS light beams        respectively comprising TM and TE mode spectra of the        near-surface waveguide; and    -   ii) an EPCS digital detector configured to sequentially detect        the sequence of TM and TE filtered and reflected EPCS light        beams to sequentially capture TM and TE images of the respective        TM and TE mode spectra of the near-surface waveguide at the        different filter wavelengths.

Another embodiment of the disclosure is directed to the EPCS systemdescribed above and herein, wherein the optical filter assemblycomprises an optical filter wheel.

Another embodiment of the disclosure is directed to the EPCS system asdescribed above and disclosed herein, wherein the optical filter wheelcomprises a plurality of optical filter assemblies each comprising anoptical filter and a correcting member configured to provide focuscorrection at the given filter wavelength.

Another embodiment of the disclosure is directed to the EPCS system asdescribed above and disclosed herein, wherein the EPCS light sourcecomprises at least one broadband light source element.

Another embodiment of the disclosure is directed to the EPCS system asdescribed above and disclosed herein, wherein the EPCS light sourcecomprises multiple light source elements that respectively emit eithersimultaneously or sequentially different EPCS light beams respectivelyhaving different wavelengths.

Another embodiment of the disclosure is directed to the EPCS system asdescribed above and disclosed herein, wherein the EPCS light beamshaving different wavelengths are combined to travel along a common axisusing one or more light-selective elements to form the multiwavelengthEPCS light beam.

Another embodiment of the disclosure is directed to the EPCS system asdescribed above and disclosed herein, wherein the one or morelight-selective elements comprises one or more dichroic mirrors.

Another embodiment of the disclosure is directed to the EPCS system asdescribed above and disclosed herein, further comprising multiplecorrection lenses respectively operably disposed relative to themultiple light source elements to facilitate optical coupling of thelight beams into the input end of the light guide.

Another embodiment of the disclosure is directed to the EPCS system asdescribed above and disclosed herein, further comprising a lightdiffuser arranged adjacent the input end of the light guide.

Another embodiment of the disclosure is directed to the EPCS system asdescribed above and disclosed herein, wherein the light guide is liquidfilled.

Another embodiment of the disclosure is directed to the EPCS system asdescribed above and disclosed herein, wherein the CS substrate comprisesa glass material, a glass-ceramic material or a crystalline material,and wherein the near-surface waveguide of the CS substrate is defined bya near-surface spike region and a deep region.

Another embodiment of the disclosure is directed to the EPCS system asdescribed above and disclosed herein, wherein the light guide assemblycomprises a light guide with an output end, the EPCS detector systemcomprises an entrance pupil, and wherein the output end of the lightguide is imaged onto the entrance pupil by the focusing optical system.

Another embodiment of the disclosure is directed to a hybrid system forcharacterizing stress in a CS substrate having a top surface and anear-surface waveguide, comprises the EPCS system as described above anddisclosed herein: a scattered light polarimetry (LSP) sub-systemcomprising a LSP light source system, an optical compensator and a LSPdetector system in optical communication with the optical compensatorthrough an LSP coupling prism having a LSP coupling surface; a couplingprism assembly comprising a prism support frame configured to operablysupport the EPCS and LSP coupling prisms so that the EPCS and LSPcoupling surfaces reside substantially in a common plane; and a supportplenum having a surface and a measurement aperture, the support plenumconfigured to support the CS substrate at a measurement plane at themeasurement aperture, and to operably support the coupling prismassembly at the measurement aperture so that the EPCS and LSP couplingsurfaces reside substantially at the measurement plane.

Another embodiment of the disclosure is directed to the EPCS system asdescribed above and disclosed herein, for characterizing stress in a CSsubstrate having a surface and a near-surface waveguide, comprising:

a) an EPCS light source system comprising:

-   -   i) an EPCS light source that emits a multiwavelength EPCS light        beam;    -   ii) an optical filter assembly configured to sequentially filter        the multiwavelength EPCS light beam to form a sequence of        filtered EPCS light beams having different filter wavelengths;    -   iii) a light guide assembly configured to transfer the sequence        of filtered EPCS light beams as guided light to a focusing        optical system arranged to receive the transferred filtered EPCS        light beams and form therefrom a sequence of filtered and        focused EPCS light beams;

b) an EPCS coupling prism that forms a EPCS coupling surface with thesurface of the CS substrate and that receives and couples the focusedsequentially filtered EPCS light beam out of the near-surface waveguideat the EPCS coupling surface to form a reflected and sequentiallyfiltered EPCS light beam that comprises at least first and second modespectra of the near-surface waveguide for the at least first and secondfilter wavelengths; and

c) an EPCS detector system comprising:

-   -   i) at least one switchable polarization filter configured to        sequentially perform transverse magnetic (TM) and transverse        electric (TE) polarization filtering of the reflected and        sequentially filtered EPCS light beam to form at least first and        second TM and TE reflected and sequentially filtered EPCS light        beams respectively comprising first and second TM and TE mode        spectra of the near-surface waveguide at the at least first and        second wavelengths, respectively; and    -   ii) at least first and second EPCS digital detectors configured        to respectively detect the at least first and second TM and TE        reflected and sequentially filtered EPCS light beams to capture        respective at least first and second TM and TE images of the        first and TM and TE mode spectra of the near-surface waveguide.

Another embodiment of the disclosure is directed to the EPCS system asdescribed above and disclosed herein, wherein the at least first andsecond EPCS digital detectors reside along respective at least first andsecond detector axes, and wherein the at least one switchablepolarization filter comprises at least first and second switchablepolarization filters respectively arranged along the at least first andsecond detector axes and upstream of the corresponding one of the atleast first and second EPCS digital detectors.

Another embodiment of the disclosure is directed to the EPCS system asdescribed above and disclosed herein, wherein the CS substrate comprisesa glass material, a glass-ceramic material or a crystalline material,and wherein the near-surface waveguide of the CS substrate is defined bya near-surface spike region and a deep region.

Another embodiment of the disclosure is directed to the EPCS system asdescribed above and disclosed herein, wherein the light guide assemblycomprises a light guide with an output end, the EPCS detector systemcomprises an entrance pupil, and wherein the output end of the lightguide is imaged onto the entrance pupil.

Another embodiment of the disclosure is directed to a system forcharacterizing stress in a CS substrate having a top surface and anear-surface waveguide, comprising: The EPCS system described above anddisclosed herein; a scattered light polarimetry (LSP) sub-systemcomprising a LSP light source system, an optical compensator and a LSPdetector system in optical communication with the optical compensatorthrough an LSP coupling prism having a LSP coupling surface; a couplingprism assembly comprising a prism support frame configured to operablysupport the EPCS and LSP coupling prisms so that the EPCS and LSPcoupling surfaces resides substantially in a common plane; and a supportplenum having a surface and a measurement aperture, the support plenumconfigured to support the CS substrate at a measurement plane at themeasurement aperture, and to operably support the coupling prismassembly at the measurement aperture so that the EPCS and LSP couplingsurfaces reside substantially at the measurement plane.

Another embodiment of the disclosure is directed to the EPCS system asdescribed above and disclosed herein, for characterizing stress in a CSsubstrate having a surface and a near-surface waveguide, comprising:

a) an EPCS light source system comprising:

-   -   i) an EPCS light source that emits a multiwavelength EPCS light        beam comprising multiple wavelengths;    -   ii) a light guide assembly that transfers the multiwavelength        EPCS light beam from the EPCS light source to a focusing optical        system arranged to receive the multiwavelength EPCS light beam        and form a focused multiwavelength EPCS light beam;

b) an EPCS coupling prism that forms an EPCS coupling surface with thesurface of the CS substrate and that receives and couples themultiwavelength EPCS light beam into and out of the near-surfacewaveguide at the EPCS coupling surface to form a reflectedmultiwavelength EPCS light beam that comprises mode spectra of thenear-surface waveguide for the corresponding multiple wavelengths of themultiwavelength EPCS light beam; and

c) an EPCS detector system comprising:

-   -   i) a switchable polarization filter operably disposed to receive        the reflected multiwavelength EPCS light beam and sequentially        form a transverse magnetic polarized (TM) multiwavelength EPCS        light beam and a transverse electric polarized (TE)        multiwavelength EPCS light beam.    -   ii) an optical filter assembly operably disposed to sequentially        filter the TM and TE multiwavelength EPCS light beams at two or        more filter wavelengths to form two or more sequentially        filtered TM and TE EPCS light beams respectively comprising the        TM and TE mode spectra of the two or more filter wavelengths;    -   iii) an EPCS digital detector configured to sequentially detect        the sequentially filtered TM and TE EPCS light beams to        sequentially capture TM and TE images of the respective TM and        TE mode spectra of the near-surface waveguide at the two or more        filter wavelengths.

Another embodiment of the disclosure is directed to the EPCS system asdescribed above and disclosed herein, wherein the CS substrate comprisesa glass material, a glass-ceramic material or a crystalline material,and wherein the near-surface waveguide of the CS substrate is defined bya near-surface spike region and a deep region.

Another embodiment of the disclosure is directed to the EPCS system asdescribed above and disclosed herein, wherein the light guide assemblycomprises a light guide with an output end, the EPCS detector systemcomprises an entrance pupil, and wherein the output end of the lightguide is imaged onto the entrance pupil by the focusing optical system.

Another embodiment of the disclosure is directed to A system forcharacterizing stress in a CS substrate having a top surface and anear-surface waveguide, comprising: The EPCS system as described aboveand disclosed herein; a scattered light polarimetry (LSP) sub-systemcomprising a LSP light source system, an optical compensator and a LSPdetector system in optical communication with the optical compensatorthrough an LSP coupling prism having a LSP coupling surface; a couplingprism assembly comprising a prism support frame configured to operablysupport the EPCS and LSP coupling prisms so that the EPCS and LSPcoupling surfaces resides substantially in a common plane; and a supportplenum having a surface and a measurement aperture, the support plenumconfigured to support the CS substrate at a measurement plane at themeasurement aperture, and to operably support the coupling prismassembly at the measurement aperture so that the EPCS and LSP couplingsurfaces reside substantially at the measurement plane.

Another embodiment of the disclosure is directed to a method ofperforming evanescent prism coupling spectroscopy for characterizingstress in a CS substrate having a surface and a near-surface waveguide,comprising:

a) forming a multiwavelength EPCS light beam having multiplewavelengths;

b) sequentially filtering the EPCS multiwavelength light beam to form asequence of filtered EPCS light beams each having a different one of themultiple wavelengths;

c) transferring the sequence of EPCS filtered light beams through alight guide to a focusing optical system to form a focused sequence ofEPCS filtered light beams;

d) directing the focused sequence of filtered EPCS light beams to anEPCS coupling prism that forms an EPCS coupling surface with the surfaceof the CS substrate and that receives and couples the sequence offiltered EPCS light beams into and out of the near-surface waveguide atthe EPCS coupling surface to form a sequence of reflected and filteredEPCS light beams that respectively comprise mode spectra of thenear-surface waveguide at one of the multiple wavelengths;

e) sequentially polarizing each of the reflected and filtered EPCS lightbeams to form for each filtered and reflected EPCS light beam atransverse magnetic (TM) filtered and reflected EPCS light beam and atransverse electric (TE) filtered and reflected EPCS light beam; and

f) sequentially digitally detecting the TM and TE filtered and reflectedEPCS light beams to sequentially capture TM and TE images of therespective TM and TE mode spectra of the near-surface waveguide for thedifferent multiple wavelengths.

Another embodiment of the disclosure is directed to the method asdescribed above and disclosed herein and further comprising processingthe sequentially captured TM and TE images of the respective TM and TEmode spectra to characterize at least one stress-related property of theCS substrate.

Another embodiment of the disclosure is directed to the method asdescribed above and disclosed herein, wherein the sequential filteringcomprises sequentially passing the multiwavelength light beam throughoptical filter assemblies supported by a filter wheel.

Another embodiment of the disclosure is directed to the method asdescribed above and disclosed herein, wherein each optical filterassembly comprises an optical filter and a correcting member configuredto correct for wavelength-dependent focus errors.

Another embodiment of the disclosure is directed to the method asdescribed above and disclosed herein, wherein the sequential polarizingcomprises passing the reflected and filtered EPCS light beams through amagnetically charged polarizing crystal operably connected to apolarization controller.

Another embodiment of the disclosure is directed to the method asdescribed above and disclosed herein, wherein the CS substrate comprisesa glass material, a glass-ceramic material or a crystalline material,and wherein the near-surface waveguide of the CS substrate is defined bya near-surface spike region and a deep region.

Another embodiment of the disclosure is directed to the method asdescribed above and disclosed herein, wherein sequentially digitallydetecting the TM and TE filtered and reflected EPCS light beams isperformed using a single EPCS digital detector.

Another embodiment of the disclosure is directed to the method asdescribed above and disclosed herein, wherein sequentially digitallydetecting the TM and TE filtered and reflected EPCS light beams isperformed using multiple EPCS digital detectors that are spatiallyseparated using dichroic mirrors.

Another embodiment of the disclosure is directed to the method asdescribed above and disclosed herein, wherein the light guide has anoutput end, the sequence of reflected filtered EPCS light beams isreceived and processed by an EPCS detector system that has an entrancepupil, and wherein the output end of the light guide is imaged onto theentrance pupil by the focusing optical system.

Another embodiment of the disclosure is directed to a light scatteringpolarimetry (LSP) system for characterizing stress in a CS substratehaving a body, a surface and a near-surface waveguide formed within thebody, comprising:

a) a LSP light source system comprising in order along a first systemaxis:

-   -   i) a laser diode that emits a LSP light beam having at least 1        microwatt of power and centered on a wavelength of 405        nanometers;    -   ii) a shutter system arranged to periodically block the LSP        light beam;    -   iii) a rotatable half-wave plate;    -   iv) a first fixed polarizer;    -   v) a first focusing lens;    -   vi) a light diffuser;    -   vii) a second focusing lens

b) an optical compensator arranged downstream of the LPS light sourceand configured to impart to the LSP light beam a time-varyingpolarization, the optical compensator comprising in order along thesystem axis:

-   -   i) a polarizing beam splitter arranged to receive the LSP light        beam from the LSP light source and transmit a first portion of        the LSP light beam along the first system axis and to direct a        second portion of the LSP light beam along a spectrometer axis;    -   ii) a spectrometer arranged along the spectrometer axis and        arranged to receive and spectrally process the second portion of        the LSP light beam;    -   iii) a second fixed polarizer;    -   iv) a variable polarizer that imparts the time-varying        polarization to the LSP light beam to form a time-varying        polarized LSP light beam;

c) an axially movable focusing lens arranged downstream of the opticalcompensator and configured to receive and focus the time-varyingpolarized LSP light beam form a focused time-varying polarized LSP lightbeam;

d) an LSP coupling prism interfaced with surface of the CS substrate toform a LSP coupling interface, wherein the focused time-varyingpolarized LSP light beam is focused at the LSP coupling interface togenerate scattered light from stress-induced features within the body ofthe CS substrate;

e) a LSP detector system arranged downstream of the LSP coupling prismand arranged to receive the scattered light, the LSP detector systemcomprising:

-   -   i) a LSP digital detector; and    -   ii) a collection optical system that collects and directs the        scattered light to the LSP digital detector to form an LSP image        at the digital detector.

Another embodiment of the disclosure is directed to the LSP system asdescribed above and as disclosed herein, wherein the variable polarizercomprises a liquid crystal variable retarder (LCVR) operably connectedto a polarization controller.

Another embodiment of the disclosure is directed to the LSP system asdescribed above and as disclosed herein, wherein the LCVR is in operablecommunication with a temperature controller that maintains the LCVRwithin a select temperature range.

Another embodiment of the disclosure is directed to the LSP system asdescribed above and as disclosed herein, wherein the select temperaturerange is between 35° C. and 40° C.

Another embodiment of the disclosure is directed to the LSP system asdescribed above and as disclosed herein, wherein the axial movablefocusing lens comprises a lens element supported by a lens support andwherein the lens support is mechanically attached to a linear motor.

Another embodiment of the disclosure is directed to the LSP system asdescribed above and as disclosed herein, wherein LSP light beam has atleast 10 microwatts of power.

Another embodiment of the disclosure is directed to the LSP system asdescribed above and as disclosed herein, wherein LSP light beam has atleast 50 microwatts of power.

Another embodiment of the disclosure is directed to a system forcharacterizing stress in a CS substrate having a top surface and anear-surface waveguide, comprising: The LSP as described above and asdisclosed herein; an evanescent prism coupling spectroscopy (EPCS)sub-system comprising a EPCS light source system and a EPCS detectorsystem in optical communication through an EPCS coupling prism having aEPCS coupling surface; a coupling prism assembly comprising a prismsupport frame configured to operably support the EPCS and LSP couplingprisms so that the EPCS and LSP coupling surfaces resides substantiallyin a common plane; and a support plenum having a surface and ameasurement aperture, the support plenum configured to support the CSsubstrate at a measurement plane at the measurement aperture, and tooperably support the coupling prism assembly at the measurement apertureso that the EPCS and LSP coupling surfaces reside substantially at themeasurement plane.

Another embodiment of the disclosure is a method of performing lightscattering polarimetry (LSP) for characterizing stress in a CS substratehaving a body, a surface and a near-surface waveguide that formsstress-related features within the body, comprising: generating a lightbeam from a laser diode having an output power of at least 1 microwattand a center wavelength of 405 nm; directing a first portion of thelight beam to a spectrometer to measure a wavelength of the light beamand an amount of power in the light beam; imparting to a second portionof the light beam a time-varying polarization using atemperature-controlled liquid crystal variable retarder (LCVR) to form atime-varying polarized light beam; focusing the time-varying polarizedlight beam onto a coupling surface formed by a coupling prism interfacedto the surface of the CS substrate to form scattered light from thestress-related features within the body of the CS substrate; anddirecting the scattered light to a digital detector to capture an LSPimage at the digital detector.

Another embodiment of the disclosure is directed to the method asdescribed above and as disclosed herein, wherein the body of the CSsubstrate is made of a glass material.

Another embodiment of the disclosure is directed to the method asdescribed above and as disclosed herein, further comprising maintainingthe LCVR at temperature in the range from 35° C. to 40° C.

Another embodiment of the disclosure is directed to the method asdescribed above and as disclosed herein, wherein the time-varyingpolarized light beam follows a beam path through the body of the CSsubstrate and further comprising estimating a beam center of the lightbeam by: performing a tilted Gaussian fit to the scattered light forselect depths into the body of the CS substrate along the beam path todefine a first set of beam centers; and fitting a first line through thefirst set of beam centers to define a first fitted line.

Another embodiment of the disclosure is directed to the method asdescribed above and as disclosed herein, further comprising estimating acenter point of the time-varying polarized light beam by fitting asecond line through a second set of beam centers to define a secondfitted line, and identifying the center point where the first and secondfitted lines cross.

Another embodiment of the disclosure is directed to the method asdescribed above and as disclosed herein, wherein the time-varyingpolarized light beam follows a beam path through the body of the CSsubstrate and further comprising determining an entrance point of thetime-varying polarized light beam into the CS substrate by: Identifyingan edge intensity profile of the LSP image along one of the first andsecond fitted lines where the edge intensity transitions from a maximumvalue I_(MAX) to a minimum value I_(MIN) representative of a backgroundintensity value; and determining a half-maximum intensity value I_(1/2)midway between the maximum and minimum intensity values I_(MAX) andI_(MIN) and defining the entrance point to be at the half-maximumintensity value I_(1/2).

Another embodiment of the disclosure is directed to the method asdescribed above and as disclosed herein, wherein the LSP light beam hasat least 10 microwatts of power.

Another embodiment of the disclosure is directed to the method asdescribed above and as disclosed herein, wherein the LSP light beam hasat least 50 microwatts of power.

Additional features and advantages are set forth in the DetailedDescription that follows, and in part will be apparent to those skilledin the art from the description or recognized by practicing theembodiments as described in the written description and claims hereof,as well as the appended drawings. It is to be understood that both theforegoing general description and the following Detailed Description aremerely exemplary, and are intended to provide an overview or frameworkto understand the nature and character of the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings are included to provide a furtherunderstanding, and are incorporated in and constitute a part of thisspecification. The drawings illustrate one or more embodiment(s), andtogether with the Detailed Description explain principles and operationof the various embodiments. As such, the disclosure will become morefully understood from the following Detailed Description, taken inconjunction with the accompanying Figures, in which:

FIG. 1A is an elevated view of an example transparent CS substrate inthe form of a planar sheet.

FIG. 1B is an example refractive index profile n(z) versus z of anexample transparent CS substrate showing a near-surface spike region(R1), a deeper region (R2) and a bulk region (R3), with a knee (KN) atthe transition between the regions R1 and R2.

FIG. 2A is a schematic diagram of the hybrid EPCS-LSP measurement systemas disclosed herein for fully characterizing the stress of a transparentCS substrate.

FIG. 2B is a more detailed schematic diagram of the hybrid EPCS-LSPsystem of FIG. 2A, showing example configurations for the EPCSmeasurement sub-system and the LSP measurement sub-system.

FIG. 3A is a schematic diagram of an example EPCS sub-system of thehybrid EPCS-LSP system of FIG. 2A.

FIG. 3B is a schematic diagram of an example EPCS mode spectrum obtainedby the EPCS sub-system, wherein the EPCS mode spectrum includes a TMmode spectrum with TM mode lines (fringes) and a TE mode spectrum withTE mode lines (fringes).

FIGS. 4A, 4B, and 4C are schematic diagrams of example LSP sub-systemsof the hybrid EPCS-LSP system of FIG. 2A.

FIG. 4D is a close-up view of an LSP image formed on the digitaldetector of the LSP sub-system, wherein the LSP image includes two lineimages that form a cross or an “X” pattern, and wherein the LSP imageand digital detector form a digital LSP image.

FIG. 5A is an elevated view of an example prism support structure forsupporting the EPCS and LSP coupling prisms.

FIG. 5B is an elevated view of a cover plate mounted on the prismsupport structure of FIG. 5A.

FIGS. 6A and 6B are side views of the EPCS and LSP coupling prismssupported on a stable platform and illustrating an example method offorming a unitary molded prism support structure for the coupling prismassembly.

FIG. 6C is a side view of an example coupling prism assembly wherein theprism support structure is configured so that at least one of the EPCSand LSP coupling prisms is movable in one direction (e.g., thez-direction, as shown) relative to the other

FIG. 6D is a schematic diagram of an example hybrid EPCS-LSP measurementsystem wherein a single coupling prism is used for the EPCS sub-systemand the LSP sub-system instead of two separate coupling prisms.

FIG. 7 is a cross-sectional view of an example prism support structureattached to an example support plenum of the hybrid system and showingan example movable substrate holder used to adjust measurement positionon the CS substrate.

FIG. 8A is an elevated view of the support plenum showing themeasurement aperture and pressure-vacuum (PV) bars of a vacuum systemoperably disposed within the measurement aperture to pneumaticallyengage the CS substrate to pull the CS substrate onto the couplingsurfaces of the EPCS and LSP coupling prisms.

FIG. 8B is a close-up cross-sectional view of the support plenum and themeasurement aperture showing an example configuration of the couplingprism assembly and the vacuum system.

FIG. 9 is a schematic representation of an example user interface aspresented by the system controller, wherein the user interface includesa EPCS section that shows the EPCS mode spectrum and an LSP section thatshows the LSP line images of the digital LSP image.

FIG. 10A is an example of an LSP section of the user interface showingan example digital LSP image and an intensity histogram of the digitalLSP image.

FIG. 10B shows an example initial or raw digital LSP image along with aGaussian-blurred (“blurred”) LSP image.

FIG. 10C shows an example threshold image as obtained by applying Ostuthresholding to the Gaussian-blurred image of FIG. 10B.

FIGS. 10D and 10E show an example of performing contour detection on anexample Gaussian-blurred LSP image.

FIG. 11A is a close-up view of the CS substrate and the direction of thefocused LSP light beam.

FIG. 11B is a close-up view of the edge portion of the CS substrate andshowing the viewing angle of the LSP detector system relative to thefocused LSP light beam.

FIG. 11C is similar to FIG. 11B and shows the scattered light beams thatreach the LSP detector system and form the line images.

FIG. 11D shows another view of the LSP detector system and the CSsubstrate with the focused LSP light beam.

FIG. 11E is a schematic diagram showing dimensions and angles used todetermine the CS substrate thickness.

FIG. 12A is a plot of the average computation time T in milliseconds(ms) needed to extract the phase φ of a noisy LSP signal versus thenoise factor N for both the lock-in method (blue) and the sine method(green).

FIG. 12B is a plot of the absolute phase difference |Δφ| for versus thenoise factor for the lock-in method (blue) and the sine method (green)for processing a noisy LSP signal.

FIGS. 13A and 13B are plots of the optical retardation OR (radians)versus the depth D (mm) into the CS substrate (“OR vs. D plots”), withFIG. 13A showing OR data collected by the LSP sub-system without usingspeckle reduction and FIG. 13 showing OR data collected by the LSPsub-system using speckle reduction.

FIGS. 14A and 14B are OR vs. D plots illustrating an example method ofshifting the OR data to make the bend points BP1 and BP2 be symmetricaround the mid-plane of the CS substrate.

FIG. 15A is an example OR vs. D plot that includes discrete data points(circles) and a fitted line to the OR vs. D data points, wherein thefitted line is formed using the “LinQuad” method disclosed herein.

FIG. 15B is a plot of the stress S (MPa) versus depth D (mm) based onthe LinQuad fit to the OR vs. D data points of FIG. 15A.

FIG. 16A is an example OR vs. D plot that includes discrete data points(circles) and a fitted line to the OR vs. D data points, wherein thefitted line is formed using the power-spike method disclosed herein.

FIG. 16B is a plot of the stress S (MPa) versus depth D (mm) (“S vs. Dplot”) based on the power-spike fit to the OR vs. D data points of FIG.16A.

FIGS. 17A and 17B are OR vs. D plots that show LinQuad curve fits to theoriginal (raw) OR vs. D data points (FIG. 17A) and to the OR vs. D datawith the symmetric component removed (FIG. 17B).

FIGS. 18A and 18B are OR vs. D plots that illustrate using reduced areafitting regions when calculating a select stress parameter, with FIG.18A showing reduced-area fitting regions at the bend points BP1 and BP2to calculate the depth of compression DOC and FIG. 18B showing areduced-area fitting region between the bend points BP1 and BP2 tocalculate the central tension CT.

FIG. 19A is a OR vs. D plot and FIG. 19B is the corresponding S vs. Dplot, wherein the curve fitting is done for the entire set of OR data.

FIG. 19C is a OR vs. D plot and FIG. 19D is the corresponding S vs. Dplot, wherein the curve fitting is done for reduced set of OR data thatexcludes portions of the data near the opposite end points.

FIG. 20 is similar to FIG. 3A and illustrates an embodiment of the EPCSsub-system wherein the detector system includes an adjustable focusinglens, wherein the adjustability includes at least one of axial movementand changing the focal length.

FIGS. 21A and 21B are schematic illustrations of example support membersuse to form a focusing lens assembly for the EPCS sub-system to providea means for adjusting the contrast of the captured mode spectrum.

FIG. 22A and FIG. 22B are similar to FIG. 3A and illustrate examples ofan enhanced EPCS sub-system that employs a light guide assembly.

FIG. 22C is a close-up schematic diagram of an example configuration ofthe EPCS sub-system employing Kohler illumination with respect to theoutput end of the light guide and an entrance pupil of the EPCS detectorsystem.

FIG. 23 is a schematic diagram of an example embodiment of the remotelight source of the EPCS sub-system.

FIG. 24A is a front-on view of a filter wheel employed in the opticalfilter apparatus in the remote light source system of FIG. 23.

FIG. 24B shows two example sequentially filtered EPCS light beams, withthe top example formed using four filter wavelengths and the bottomexample formed using two filter wavelengths as formed using the remotelight source of FIG. 23.

FIGS. 25A through 25C illustrates example configurations of the EPCSdetector system for the enhanced EPCS sub-system.

FIG. 26 is similar to FIG. 4A and illustrates an example of an enhancedLSP sub-system.

FIG. 27A is a schematic diagram of an example power monitoring systemthat can be implemented in the enhanced LSP sub-system of FIG. 26.

FIG. 27B is a plot of the (normalized) optical power OP versuspolarization angle (degrees) for transmitted and reflected portions ofthe light beam for the power monitoring system of FIG. 27A.

FIG. 28 is a plot of the central tension CT (MPa) versus the lensposition LP (mm) (relative to a reference position) for the axiallymovable focusing lens, showing a variation in the CT with lens positionand thus illustrating the importance of providing a proper focus for thefocused LSP light beam.

FIG. 29 is similar to FIG. 11B and shows measurement parameters for theLSP detector system relative to the CS substrate for performing acalibration process.

FIG. 30A is a plot of the intensity I(p) versus pixel location p(x) inthe x-direction along an LSP beam for a select depth in the CS substrateand showing an example of a tilted Gaussian fit to the measuredintensity to estimate the center of the LSP light beam as indicated bythe large black dot at the peak of the fitted curve (solid line).

FIG. 30B is a plot of the pixel locations p(x) and p(y) of the peakcenters as determined by the method associated with FIG. 30A.

FIG. 30C is a schematic diagram similar to FIG. 10C that shows an LSPimage (intensity contour) with two superimposed fit lines (FL1 and FL2)running through the center of the two line-image sections, with theintersection of the two fitted lines representing the center point ofthe LSP image.

FIG. 30D is a plot of the LSP image intensity I(p) vs. pixel position palong the fitted line FL2 and in the vicinity of the entrance point EPand illustrates an example edge intensity profile having a maximumintensity I_(MAX), a minimum intensity I_(MIN), and the half-maximumintensity I_(1/2), which resides midway between I_(MAX) and I_(MIN) anddefines the position (pixel location) of an entrance point ENP, which inthe example plot is about at pixel 32.

DETAILED DESCRIPTION

Reference is now made in detail to various embodiments of thedisclosure, examples of which are illustrated in the accompanyingdrawings. Whenever possible, the same or like reference numbers andsymbols are used throughout the drawings to refer to the same or likeparts. The drawings are not necessarily to scale, and one skilled in theart will recognize where the drawings have been simplified to illustratethe key aspects of the disclosure.

The claims as set forth below are incorporated into and constitute partof this Detailed Description.

Cartesian coordinates are shown in some of the Figures for the sake ofreference and are not intended to be limiting as to direction ororientation.

In some parts of the discussion, the z coordinate is used for the depthdirection into the substrate, while in other parts of the discussion adifferent coordinate is used.

The acronym “IOX” stands for “ion exchange” or “ion exchanged,”depending on the context of the discussion.

The acronym “CS” when used to described a type of substrate (as in “CSsubstrate”) means “chemically strengthened.” The acronym CS can alsomean “compressive stress,” and which meaning is being used for thisacronym will be apparent by the context of the discussion.

The term “strengthened” for the CS substrates considered herein meansthat the original CS substrates have undergone a process to create somestress profiles that could have a variety of shapes, typically intendedto make the CS substrates stronger and thus harder to break. Examplestrengthening processes include ion exchange, tempering, annealing andlike thermal processes.

The term “transparent” as used in reference to the CS substrate means aCS substrate that has sufficient optical transmission at the givemeasurement wavelength (i.e., the EPCS wavelength λ_(A) or the LSPwavelength λ_(B)) to make the satisfactory measurement (i.e., an EPCSmeasurement or a LSP measurement) of the CS substrate that yields asufficiently accurate measurement of the stress characteristicsassociated with the given measurement.

The abbreviation “ms” stands for “millisecond.”

The abbreviation “nm” stands for “nanometer.”

The term “near-surface” such as when referring to a near-surfacewaveguide or a near-surface spike region of the CS substrate, refers tothe portion of the substrate body that resides immediately adjacent agiven surface (e.g., the top or measurement surface) of the CSsubstrate.

In an example, a glass-based substrate is used to form the CS substrate.The term “glass-based substrate” as used herein includes any object madewholly or partly of glass, such as laminates of glass and non-glassmaterials, laminates of glass and crystalline materials, andglass-ceramics (including an amorphous phase and a crystalline phase).Thus, in an example, the glass-based CS substrate” can consist entirelyof a glass material while in another example can consist entirely of aglass-ceramic material.

The terms “image” and “line image” are used herein to describe adistribution of light (i.e., intensity distribution) of a portion of theX-shaped LSP image as formed by scattered light at digital detector (CCDcamera or CMOS sensor, etc.) by the LSP sub-system, and an imagingsystem is not necessary to form the LSP image as considered herein.

In the discussion below, the LSP sub-system is configured to cyclebetween two or more polarization states (or just “polarizations” forshort). In an example, there can be up to eight different polarizationstates per cycle that combine the linear, elliptical and circularpolarizations as is known in the art.

The term “stress” as used herein can generally mean compressive stressor tensile stress. In the plots of FIGS. 15B, 16B, 19B and 19D, thecompressive stress is negative while the tensile strength is positive.Whether the stress is compressive or tensile depends on the location ordepth region of the CS substrate under consideration. A positive valuefor the compressive stress is understood to mean the magnitude of thecompressive stress. The stress is denoted by S or by σ and is taken torefer to the compressive stress unless otherwise noted or as otherwiseunderstood by the context of the discussion. In some instances, thecompressive stress is denoted CS, such as for the knee stress CS_(k).The stress profile is the stress S as a function of depth into the CSsubstrate, and the depth coordinate can be any local coordinate, and inthe discussion below both z and x are used as the local coordinate.

In an example, the “characterizing” of a CS substrate includesdetermining one or more stress-based properties of the CS substrate,such as a stress profile S(z), a depth of layer DOL, a surface stressS(0), a depth of compression DOC, a central tension CT, and abirefringence profile B(z). In an example, the characterizing utilizesboth EPCS and LSP measurements that respectively provide first andsecond stress characteristics that when combined provide a “fullcharacterization” of the stress characteristics of the CS substrate,wherein the term “full characterization” means a more completecharacterization of the stress and stress-related properties than ispossible with just the first stress characteristics of the EPCSmeasurements or just the second stress characteristics of the LSPmeasurements.

The acronym “OR” stands for “optical retardation” and is measured inradians (“rads”) unless otherwise stated. Plots of the opticalretardation versus depth into the CS substrate are referred to below as“OR vs. D” curves or plots, where D is understood as being the depthinto the CS substrate body from the top (measurement) surface.

The term “index-matching fluid” means a fluid with a refractive indexsubstantially the same as another material to facilitate opticalcoupling. In an example, the index-matching fluid comprises an oil or amixture of oils. The refractive index of the index-matching fluid isdenoted by either n_(f) or n_(oil), i.e., these two expressions are usedinterchangeably below.

The term “plate” and “waveplate” can used interchangeably when referringto types of waveplates (e.g., a half-wave plate is the same as ahalf-wave waveplate, etc.). To avoid confusion, the term “waveplate” isreferred below to below as a “plate” when the proceeding term includesthe word “wave.”

The term “sub-system” is used in places where convenient to distinguishfrom a larger system in which a smaller system resides. Thus, the terms“system” and “sub-system” are used interchangeably for ease ofdiscussion.

The CS Substrate

FIG. 1A is an elevated view of an example type of CS substrate 10 in theform of a planar sheet. The CS substrate 10 has a body 11, a top surface12, a bottom surface 14 and sides 16. The CS substrate 10 has athickness TH and a mid-plane MP half way between the top surface 12 andbottom surface 14 and parallel thereto.

In some cases, the thickness TH can be in the range from 0.050 mm TH 2mm, such as 0.20 mm≤TH≤2 mm, 0.25 mm≤TH≤2 mm, 0.3 mm≤TH≤2 mm, or 0.3mm≤TH≤1 mm, and any and all sub-ranges formed between these endpoints.

Example types of CS substrates 10 are glass-based and are used asprotective covers for displays and/or housings for mobile devices suchas smart phones, tablets, laptop computers, GPS devices, etc. Such CSsubstrates 10 tend to be thin and planar, such as shown in FIG. 1A.

The CS substrate 10 includes a near-surface waveguide (NSWG) 18 thatresides in the body 11 proximate the top surface 12. In an example, theNSWG 18 is formed using an IOX process and is defined by at least oneIOX region of varying refractive index.

FIG. 1B is a plot of the refractive index n versus the depth z into theCS substrate for an example NSWG 18. The surface refractive index isdenoted n_(s) while the bulk refractive index, i.e., the refractiveindex of the substrate material that has not been affected by thechemical strengthening process is denoted n_(B).

The plot of FIG. 1B shows an example refractive index profile n(z) thatdefines two (IOX) regions, namely a first near-surface spike region R1and a second deep region R2. There is also a third region R3 deeper thanthe second deep region and it is referred to herein as the “bulk” regionhaving the refractive index n_(B). The near-surface spike region R1 hasa maximum refractive index n_(s) at the surface and a rapid decrease inthe refractive index with depth (z) to a value n_(k) over a relativelyshallow depth z=D1 that defines a first “spike” depth of layer DOL_(sp).The deep region R2 has a slower decrease in the refractive index fromn_(k) down to a depth D2 that defines a total depth of layer DOL_(T)where the third bulk region R3 starts. The first and second regions R1and R2 meet at (and thus define) a knee KN at z=Z_(k) where as notedabove the refractive index n=n_(k) and which is associated with a knee(compressive) stress CS_(k).

Because of the two distinct refractive-index regions R1 and R2 in theNSWG 18, certain guided modes propagate only in the uppermost spikeregion R1 while other guided modes travel in both regions R1 and R2,while still other guided modes travel only in the deep region R2. Otherrefractive index profiles n(z) include more uniform changes in therefractive index. Some of the deep guided modes can extend into the bulkregion R3.

The refractive index profile n(z) of FIG. 1B can be formed by a dual IOX(DIOX) process where one IOX process forms the deep region R2 andanother IOX process different from the first IOX process forms the spikeregion R1. The plot of FIG. 1B is representative of a DIOX processcarried out in Li-containing glass CS substrate 10 wherein Li ions areexchanged with potassium and sodium ions in two distinct IOX processes,with the potassium IOX process generating the spike region R1.

The Hybrid EPCS-LSP System

FIG. 2A is a schematic diagram of the hybrid EPCS-LSP measurement system(“hybrid system”) 20 as disclosed herein shown along with an example CSsubstrate 10. The hybrid system 20 includes a coupling prism assembly40, an EPCS measurement sub-system (“EPCS sub-system”) 100, a LSPmeasurement sub-system (“LSP sub-system”) 200, and a system controller400. The coupling prism assembly 40 defines a measurement location ML onthe CS substrate 10.

The EPCS sub-system 100 generates a EPCS measurement signal SArepresentative of first stress characteristics of the CS substrate atthe measurement location ML as embodied in a mode spectrum of the guidedmodes of the NSWG 18. The first stress characteristics can include oneor more of the following: a surface compressive stress S(0), a totaldepth of layer DOL_(T), a spike depth of layer DOL_(sp), a knee stressCS_(k) and a birefringence B.

The LSP sub-system 200 generates a LSP measurement signal SBrepresentative of second stress characteristics of the CS substrate atthe measurement location ML as embodied in optical retardation (OR)information as a function of depth into the CS substrate, including thedeep region R2. The second stress characteristics can include one ormore of the following: a stress profile, a depth of compression DOC anda central tension CT.

In an example, EPCS and LSP measurements of the first and second stresscharacteristics are made without moving the measurement location ML. Inanother example, the EPCS and LSP measurements of the first and secondstress characteristics are made by translating the coupling prismassembly 40 such that the EPCS and LSP measurements are made at the sameposition on the substrate rather than at slightly spaced part positionsat the measurement location as defined by the configuration of thecoupling prism assembly.

In an example, the EPCS and LSP measurements of the first and secondstress characteristics are made without removing either the couplingprism assembly 40 or the CS substrate 10 from the measurement locationML. This represents an advantage over the prior art in that both EPCSand LSP measurements can be made in a single system without having toremove or otherwise handle the CS substrate to bring it to a differentmeasurement system.

The EPCS and LSP measurement signals SA and SB are sent to the systemcontroller 400 for processing. The system controller 400 can comprisefor example a micro-controller, computer, programmable logic controller(PLC), etc. In an example, the system controller 400 is configured withinstructions embodied in a non-transitory computer-readable medium(e.g., software) to control the operation of the hybrid system 20 andperform the calculations for determining the first and second stresscharacteristic of the CS substrate 10 based on the EPCS and LSPmeasurement signals SA and SB.

In an example, the system controller 400 processes the EPCS and LSPmeasurement signals SA and SB to define a stress profile and relatedstress characteristics from the top surface 12 of the CS substrate 10down to at least the bottom of the deep region R2. In other words, thesystem controller combines the first and second stress characteristicsobtained from EPCS sub-system 100 and the LSP sub-system 200 to generatea more complete or “full” stress profile of the CS substrate than ispossible with just one of the measurement sub-systems.

The coupling prism assembly 40 includes a EPCS coupling prism 42A and aLSP coupling prism 42B operably supported by a prism support structure46. The coupling prism assembly 40 is operably disposed on or proximatethe top surface 12 of the CS substrate 10. In examples discussed below,the EPCS coupling prism 42A and the LSP coupling prism 42B can beseparate coupling prisms or different sections of a single (common)coupling prism.

With continuing reference to FIG. 2A, the hybrid system 20 includes anexample housing 21 having dimensions L1 and L2. Example dimensions forL1 and L2 are in the range from 8 inches to 12 inches for a relativelycompact embodiment of the hybrid system 20.

The EPCS sub-system 100 includes a EPCS light source system 110 and aEPCS detector system 140 optically coupled via the EPCS coupling prism42A. The LSP sub-system 200 includes a LSP light source system 210, anoptical compensator 230 and a LSP detector system 240 optically coupledto the optical compensator via the LSP coupling prism 42B. The EPCS andLSP detector systems 140 and 240 are operably connected to the systemcontroller 400. Examples of the EPCS sub-system 100 is described in U.S.Pat. No. 9,534,981 and in U.S. Pat. No. 9,696,207, which areincorporated by reference herein. Examples of the LSP sub-system 200 aredescribed in U.S. Pat. No. 4,655,589, and in U.S. Provisional PatentApplication Ser. No. 62/753,388, which are incorporated by referenceherein.

FIG. 2B is a more detailed schematic diagram of the hybrid EPCS-LSPsystem of FIG. 2A, showing example configurations for the EPCSsub-system 100 and the LSP sub-system 200. FIG. 3A is a schematicdiagram of example EPCS sub-system 100. FIGS. 4A through 4C areschematic diagrams of example LSP sub-systems 200.

The EPCS Sub-System

With reference to FIG. 2B and FIG. 3A, the EPCS light source system 110of the EPCS sub-system 100 includes a EPCS light source 112 thatgenerates a EPCS light beam 116 at a first wavelength λ_(A) along afirst axis A1. The first wavelength λ_(A) can also be referred to as theEPCS wavelength.

The EPCS light source system 110 also includes along the first opticalaxis A1: an optional polarizer 118, a light diffuser 122 that residesdownstream of the EPCS light source 112, and a focusing lens 120 thatresides downstream of the light diffuser. In an example, the lightsource comprises a light-emitting diode (LED), and further in an examplethe LED operates at an EPCS measurement wavelength λ_(A) of 365 nm. TheEPCS detector system 140 resides along a second axis A2 and includes inorder along the second axis: a focusing lens 142, a band-pass filter 144centered on the wavelength λ_(A), an attenuator 146, a TM-TE polarizer148 (which has TM and TE sections, not shown) and a digital detector(e.g., a digital camera, image sensor, CCD array, etc.) 150 that has TMand TE sections (not shown) as defined by the TM-TE polarizer 148.

The EPCS light beam 116 from the EPCS light source 112 is diffused bythe light diffuser 122 and is focused by the focusing lens 120 to form afocused EPCS light beam 116F. The focused EPCS light beam 116F isincident upon the EPCS coupling prism 42A at an input surface 43A. Thiscouples the EPCS focused light beam into the NSWG 18 at a first (EPCS)coupling interface INT1 defined by the top surface 12 of the CSsubstrate and a bottom or “coupling” surface 45A of the EPCS couplingprism 42A. The first coupling interface INT1 can include anindex-matching fluid 5A, as discussed in greater detail below.

A reflected EPCS light beam 116R is formed from the focused EPCS lightbeam 116F at the first EPCS coupling interface INT1 and exits the outputsurface 44A of the EPCS coupling prism 42A to travel along a second axisA2. The first and second axes A1 and A2 residing in a common plane(e.g., x-z plane of FIG. 3A). The reflected EPCS light beam 116Rincludes information about the mode spectrum of the guided modes of theNSWG 18. The reflected EPCS light beam 116R is focused by the focusinglens 142 in the EPCS detector system 140 to form an image of the modespectrum of the guided light at the EPCS digital detector 150.

The band-pass filter 144 assures that only the reflected EPCS light beam116R makes it through to the EPCS digital detector 150. The attenuator146 assures that the detected reflected EPCS light beam 116R has theappropriate intensity distribution for efficient digital detection. TheTM-TE polarizer 148 defines TM and TE sections for the digital detectorso that TM and TE mode spectra can be captured by the EPCS digitaldetector 150. The TM and TE mode spectra are embodied in the firstdetector signal SA sent to the system controller 400 for processing. Itis noted that the order of the band-pass filter 144, the attenuator 146and the focusing lens 142 is not critical and is intentionally shown asbeing different between FIGS. 2B and 3A to illustrate this point.

FIG. 3B is a schematic representation of an idealized mode spectrum 160as captured by the EPCS digital detector 150. Local (x,y) Cartesiancoordinates are shown for reference. The mode spectrum 160 has TM and TEtotal-internal-reflection (TIR) sections 161TM and 161TE respectivelyassociated with TM and TE guided modes, and non-TIR sections 162TM andTE respectively associated with TM and TE radiation modes and leakymodes. The TIR section 161TM includes one or more TM “fringe” or TM modelines 163TM while the TIR section 161TE includes one or more TE“fringes” or TE mode lines 163TE. The TM and TE mode lines 163TM and163TE are generally aligned in the x direction and are spaced apart inthe y direction.

Transition regions (“transitions”) 166TM and 166TE between the TIRsection 161TM, 161TE and the non-TIR sections 162TM, 162TE define acritical angle for the optical coupling into and out of the NSWG 18 ofthe CS substrate 10 for TM and TE polarized light, and are referred toas the critical angle transitions. The difference in locations of thestart of the critical angle transitions 166TM and 166TE is proportionalto the knee stress CS_(k) and this is proportionality is indicated by“˜CS_(k)” in FIG. 3B.

The TM and TE mode lines 163TM and 163TE can either be bright lines ordark lines, depending on the configuration of the EPCS sub-system 100.In FIG. 3B, the TM and TE mode lines 163TM and 163TE are shown as darklines for ease of illustration.

The stress characteristics for the EPCS measurement are calculated basedon the difference in the y positions of the TM and TE mode lines 163TMand 163TE in the mode spectrum 160. The birefringence B is thedifference between the effective indices of the TM and TE polarizations,wherein the effective indices are represented by the y positions of themode lines. The surface compressive stress S(0)=CS is computed by the ydistances between the mode lines (effective indices) and the ratioB/SOC, where SOC is the stress optic coefficient. At least two TM and TEmode lines 163TM and 163TE are needed to calculate the surface stressS(0). Additional mode lines are needed to calculate the compressivestress profile S(z). The depth of layer DOL_(T) is a measure of stresspenetration or ion penetration length into the body 11 of the CSsubstrate 10, and in the case of an IOX process, can also be calculatedby the y-locations and number of mode lines 163TM and 163TE. The TM andTE mode line locations along the y axis are thus the most basicmeasurement for inferring stress-related characteristics of the CSsubstrate 10. The calculations for determining the stresscharacteristics of the CS substrate 10 based on the EPCS measurementsusing the EPCS sub-system 100 are carried out in the system controller400.

The LSP Sub-System

With reference now to FIG. 2B and FIGS. 4A through 4C, the LSP lightsource system 210 of the LSP sub-system 200 includes a LSP light source212 that generates a LSP light beam 216 of wavelength λ_(B) along athird axis A3. In an example, the LSP light source 212 is configured asa laser diode that operates at a second wavelength λ_(B)=415 nm. Thesecond wavelength λ_(B) can also be referred to as the LSP wavelength.

The LSP light source system 210 includes in order along the third axisA3: an optional neutral density filter 218 (shown in FIGS. 2B and 4A), afirst focusing lens 220, a movable light diffuser 222, and a secondfocusing lens 224. The movable light diffuser 222 can comprise aholographic element configured to perform light diffusion at thewavelength λ_(B). In an example, the movable light diffuser can compriserotating light diffuser or oscillating light diffuser. One or more foldmirrors FM can be used to fold the LSP sub-system 200 to make it morecompact.

The optical compensator 230 resides along the (folded) third axis A3 andincludes a polarizer, which can be in the form of a polarizing beamsplitter PBS 232. The optical compensator 230 also includes a half-waveplate 234H and a quarter-wave plate 234Q with one of the wave platesbeing rotatable relative to the other to change the state ofpolarization of the LSP light beam 216. In an example, the opticalcompensator 230 can comprise an electronically controlled polarizationmodulator, such as a liquid-crystal-based modulator or a ferroelectricliquid-crystal-based modulator or like modulator.

In an example, the optical compensator 230 is operably connected to orotherwise includes a controller (not shown) that controls thepolarization switching operation performed by the optical compensator.In an example, the optical compensator 230 can comprise a single liquidcrystal device. In another example, the optical compensator 230 cancomprise multiple elements such as polarizers, wave plates, filters,prisms (e.g., wedge prisms), etc. In an example, the optical compensator230 causes the LSP light beam 216 to go through a full polarizationcycle (i.e., change between two or more select polarizations) inanywhere from less than 1 second to 10 seconds. In an example, theoptical compensator 230 can be operably connected to and controlled bythe system controller 400.

A third focusing lens 236 resides downstream of the optical compensator230 and is used to form a focused LSP light beam 216F, which is directedto the LSP coupling prism 42B. The LSP coupling prism has respectiveinput and output surfaces 43B and 44B and a bottom or “coupling” surface45B. The coupling surface 45B and the top surface 12 of the CS substrate10 defines a second (LSP) coupling interface IF2. In an example, thesecond coupling interface INT2 includes an index matching fluid 5B, asdiscussed below.

The LSP detector system 240 resides along a fourth axis A4 that isorthogonal to the third axis A3, i.e., the fourth axis A4 resides in theY-Z plane.

In an example, the LSP detector system 240 includes a collection opticalsystem 243 and a digital detector (e.g., a CCD camera) 246. In anexample, the collection optical system 243 is telecentric and has unitmagnification. The LSP detector system 240 can also include a bandpassfilter 244 centered on the second wavelength λ_(B). In the example shownin FIG. 4C, the digital detector 246 comprises array of imaging pixels247, which in an example can have a dimension of between 1.8 microns and10 microns.

In the operation of the LSP sub-system 200, the focused LSP light beam216F is incident upon the input surface 43B of the LSP coupling prism42B and travels to the coupling surface 45B and then through theindex-matching fluid 5B and to the top surface 12 of the CS substrate 10to enter the body 11 of the CS substrate. The focused LSP light beam216F has a select polarization at any given time as defined by theoptical compensator 230. The (polarized) input focused LSP light beam216F is scattered by stress-induced features in the body 11 of the CSsubstrate 10 to form a scattered LSP light beam 216S. The scattered LSPlight beam 216S exits the CS substrate 10 at the top surface 12, passesback through the second coupling interface INT2 and then exits the LSPcoupling prism 42B at the output surface 44B. The scattered LSP lightbeam 216S travels to the LSP detector system 240 and is directed to thedigital detector 246 by the collection optical system 243. The scatteredLSP light beam 216S forms a LSP image 248 on the digital detector 246,as shown in the close-up view of FIG. 4D. This defines a digital LSPimage. The LSP image 248 as discussed below is taken to be the digitalLSP image unless otherwise noted. The characteristic “X” shape of theLSP image 248 is known in the art of LSP and is due to reflections ofthe scattered LSP light beam 216S from the different interfacesassociated with the LSP interface INT2 as defined by CS substrate 10,LSP coupling prism 42B and the index-matching fluid 5B.

As shown in FIG. 4D, the X shape of the LSP image 248 is defined by twocrossed line images LI each having a local length coordinate x_(L) alongits length. Each line image LI has an intensity distribution I(x_(L))that is measured by the pixels 247 that coincide with the line image.The digital detector converts the intensity distributions I(x_(L)) to asecond detector signal SB, which is sent to the system controller 400.Only one of the line images LI is needed for performing a measurement.In an example, image processing is used to identify a portion of the LSPimage 248 for use subsequent processing to extract the opticalretardation information, as explained below.

In an example, a given measurement of the CS substrate 10 using the LSPsub-system 200 includes making measurements for a measurement time t_(M)of between 1 second and 10 seconds. During the measurement time t_(M),the polarization state of the LSP light beam 216 varies between thedifferent polarization states, preferably making one or more cyclesthrough the polarization states. Meantime, for each polarization state,the digital detector 246 captures the LSP image 248 during exposuretimes t_(E). In an example, the exposure times t_(E) are about the sameas the frame rate FR of the digital detector 246. An example exposuretime t_(E)=50 ms, which corresponds to a frame rate FR=20 frames persecond. The exposure time t_(E) can also be less than the frame rate.

The electronically captured LSP images 248 differ in their intensitydistributions I(x_(L)) depending on the polarization state of the inputfocused LSP light beam 216F and the optical retardation incurred alongthe beam path. The difference is due to the difference in thedestructive and constructive interference along the length of thescattered LSP light beam 216S as a function of depth D into the CSsubstrate 10 between the different polarization states. The differencesbetween the multiple intensity distributions I(x_(L)) for the differentpolarization states is used by the system controller 400 to calculate anoptical retardance OR as a function of depth D into the body 11 of theCS substrate 10 using relationships well known in the art. Likewise,multiple optical retardance curves OR vs the depth D (“OR vs. D plots”)are calculated using the differences in the intensity distributionsI(x_(L)). For example, for a 3 second measurement time t_(M) with animage sensor frame rate FR of 20 frames/second, a total of 60 plots ofI(x_(L)) vs. D can be generated to compute OR vs. D and used tocalculate one or more stress-related characteristics of the CS substrate10.

While the intensity distributions I(x_(L)) for the LSP image 248necessarily differ between polarization states of the input light beam112, when there is stress present in the CS substrate 10, the differentOR vs. D curves (plots) as calculated from the measured intensitydistributions should ideally be the same for a given CS substrate at thegiven measurement location for CS substrates where the stress profile is(ideally) constant.

While LSP measurement technique can generate a stress profile S(z), itdoes not generally produce an accurate representation of the stressprofile in the near-surface region of the CS substrate 10. There areleast two problematic effects that present challenges for extracting anaccurate characterization of the near-surface stress profile for a CSsubstrate 10 using an LSP measurement from the LSP sub-system 200. Oneproblematic effect is referred to as a “fireball” effect, which iscaused by excessive light scattering at the LSP interface INT2. Theexcessive light scattering generates noise, which corrupts the LSPmeasurement data for near-surface region, which in an example is thefirst 60 microns to 100 micrometers below the top surface 12 of the CSsubstrate 10.

The other problematic effect is caused by the convolution of photonsscattered from different depths into the signal corresponding to aparticular depth. This convolution significantly changes the signal inthe region where stress changes fast, which is usually in thenear-surface compression region, most often in the first 80 microns, 100microns, or 150 microns, but sometimes as high as 200 microns. Theregion of fast change is thicker for larger thicknesses of Li-basedglass)

Some prior-art LSP systems attempt to decrease these convolution effectsby using a very focused beam near the CS substrate surface, with beamdiameter as small as 10 microns. Unfortunately, this leads to otherproblems—such as increased laser noise (e.g., speckle) in the same depthregion of interest, making the extracted stress profiles in thenear-surface region even less reliable.

Coupling Prism Assembly

The hybrid system 20 utilizes the aforementioned coupling prism assembly40, which operably supports the EPCS coupling prism 42A and the LSPcoupling prism 42B to provide the prism coupling for the EPCS sub-system100 and the LSP sub-system 200 when making the EPCS measurement and theLSP measurement of the CS substrate 10.

FIG. 5A is an elevated view of a top portion of an example couplingprism assembly 40 showing an example support frame 48. FIG. 5B is anelevated view similar to FIG. 5A and that additionally includes a coverplate 60. The example support frame 48 includes a EPCS frame section 48Athat supports the EPCS coupling prism 42A and a LSP frame section 48Bthat supports the LSP coupling prism 42B. The support frame 48 alsoincludes an isolation member 50 disposed between the EPCS frame section48A and the LSP frame section 48B that is configured to opticallyisolate the EPCS and LSP coupling prisms 42A and 42B. In an example, theisolation member 50 also prevents the mixing of index-matching fluids 5Aand 5B respectively used with the EPCS and LSP coupling prisms 42A and42B. In another example, the isolation member 50 allows for a singleindex-matching fluid to be used with both the EPCS and LSP couplingprisms 42A and 42B, i.e., the single index-matching fluid can flowbetween the first and second interfaces INT1 and INT2 defined by the twodifferent prisms. In one example, the isolation member 50 is a separatepart from the support frame 48 and is attached thereto. In anotherexample, the isolation member 50 is part of the support frame 48, i.e.,is formed integral therewith during the formation of the support frame.

In an example, the EPCS and LSP frame sections 48B and the isolationmember 50 including securing tabs 52 that includes mounting holes 53that allow for securing the cover plate 60 to the frame sections usingsecuring members (not shown). The cover plate 60 includes a firstaperture 62A sized to accommodate the coupling surface 45A of the EPCScoupling prism 42A and a second aperture 62B sized to accommodate thecoupling surface 45B of the LSP coupling prism 42B.

FIGS. 6A and 6B illustrate an example method wherein the EPCS and LSPframe sections 48A and 48B are formed using a resin mold process. Theprocess provides for precision alignment of the EPCS and LSP couplingprisms 42A and 42B. In an example, the molding process is carried outwith example EPCS and LSP coupling prisms 42A and 42B in place on astable platform 75. This process is discussed in greater detail below.

FIG. 7 is an x-z cross-sectional view of an example prism supportstructure 46 attached to an example support plenum 70 of the hybridsystem 20 using the securing tabs 52 and securing members 54, such asscrews, that pass through the mounting holes 53. The support plenum 70has a top surface 71 and measurement aperture 72. The top surface 71defines an example measurement plane MP at the measurement aperture 72.The prism support structure 46 is supported by the support plenum 70such that the EPCS and LSP coupling prisms 42A and 42B reside at themeasurement aperture 72. In an example, the EPCS and LSP couplingsurfaces 45A and 45B of the EPCS and LSP coupling prisms 42A and 42Breside at or substantially at the measurement plane MP.

In an example, the CS substrate 10 is operably supported by a movablesubstrate holder 80 that holds the CS substrate over the measurementaperture 72 so that the EPCS and LSP coupling prisms 42A and 42B can beinterfaced with the top surface 12 of the CS substrate 10 to establishthe first and second coupling interfaces INT1 and INT2 at orsubstantially at the measurement plane MP. In an example, the movablesubstrate holder 80 is conveyed over the top surface 71 of the supportplenum 70 using conveying elements 73 such as rollers, wheels, sliders,bearings, etc. In an example, the CS substrate 10 is supported by themovable substrate holder 80 at an interior lip 82 that supports an outer(perimeter) portion of the top surface 12 of the CS substrate. In anexample, the plane of the interior lip 82 defines an example measurementplane MP. Thus, FIG. 7 shows two different example locations of themeasurement plane MP.

FIG. 8A is an elevated view that illustrates an example wherein thesupport plenum 70 is in the form of a plate that includespressure-vacuum (PV) elements or PV conduits 90 (e.g., PV bars) used topneumatically engage the CS substrate 10 to pull the CS substrate ontothe coupling surfaces 45A and 45B of the EPCS and LSP coupling prisms42A and 42B via vacuum (negative pressure) and then release the CSsubstrate from the prisms via pressure (positive pressure). FIG. 8B is across-sectional view of the support plenum and measurement aperture ofthe configuration of FIG. 8A showing an example vacuum system 91 thatinclude the PV elements (PV bars) 90 and a vacuum source 92.

Note that the interior lip 82 of the movable substrate holder 80 definesa stop member for limiting the vertical movement of the CS substrate 10when a vacuum is applied to the CS substrate via the vacuum system 91.

Hybrid System Employing a Single Index-Matching Fluid

An example embodiment of the hybrid system 20 such as shown in FIG. 6Demploys a single index-matching fluid 5 of refractive index n_(f) forboth EPCS and LSP sub-systems 100 and 200. This is a counter-intuitiveapproach since a single index-matching fluid 5 would typically beconsidered as not being able to produce good measurement results fromboth sub-systems at the same time for at least the following reasons.

If the index-matching fluid is chosen based on EPCS measurementconsiderations, the index matching fluid has a refractive index n_(f)that is substantially higher (e.g., by 0.1 or more) than the surfacerefractive index n_(s) of CS substrate to facilitate coupling of lightinto the guided modes and to obtain good fringe contrast in the capturedTM and TE mode spectra.

On the other hand, this level of refractive index contrast (difference)Δn between refractive indices of the index-matching fluid 5 and the topsurface 12 of the CS substrate 10 causes significant surface scatteringat the coupling interface INT2 from beam deflection at the indexmismatch associated with the micro-roughness of the surfaces. This isproblematic for the accurate extraction of retardation and stressmeasurements at moderate depths based on receiving and processingscattered light from the CS substrate. The high degree surfacescattering produces a “fireball”, e.g., a large bright spot on the imageof the scattered light beam where the pixels 247 of the digital detector(CCD camera) 246 are saturated with photons. This results in the loss ofa substantial amount of stress-related information. Well-polishedsurfaces or pristine surfaces (such as formed by fusion drawing) tend tohave less scattering.

If the index-matching fluid n_(f) is approximately matched to (e.g.,being similar, slightly higher, or slightly lower than) the surfacerefractive index n_(s) of the CS substrate 10 to ensure low surfacescattering, the fringe contrast in the mode spectrum 160 is usually poorwhen there is a steep change in the refractive index near the surface,e.g., such as the spike region R1 (see FIG. 1B) as caused by a shallowconcentrated spike of K₂O concentration as produced by an IOX process.Furthermore, the position and contrast of the TM and TE fringes 163TMand 163TE become dependent on the thickness of the index-matching fluid.These two effects make it very difficult to measure the surface CS andspike DOL accurately using the EPCS sub-system 100.

If the index-matching fluid 5 is chosen to have a refractive index n_(f)lower than the substrate (bulk) refractive index n_(B) of the CSsubstrate 10 (which also usually means lower than the surface refractiveindex), then the thickness of the index-matching fluid must be verysmall (e.g., less than 0.4 micron) to enable light coupling into thewaveguide modes of the near-surface portion (spike region R1) of theNSWG 18 for the surface CS measurement. The small thickness is alsorequired for measuring the critical angle for coupling light thattravels in the deep region R2 between the surface spike region R1 andthe bulk region R3. This is difficult to achieve consistently in aproduction environment due to issues with small particle contamination.These issues cause problems for accurately measuring the surface(compressive) stress S(0) and the “knee stress” S_(k) at the bottom ofthe surface refractive-index spike region R1 for dual IOX Li-containingglasses and glass ceramics.

It turns out a single index-matching fluid 5 for both EPCS and LSPmeasurements can be used under select conditions wherein the spikeregion R1 of the CS substrate 10 has a normalized slopeS_(n)=|(λ/n)dn(z)/dz|<0.0005, or more preferably S_(n)<0.0004, where λis the measurement wavelength and n(z) is the index of refraction of theCS substrate 10 at the measurement wavelength.

In one embodiment, an index-matching fluid 5 having a refractive indexn_(f) that is higher (greater) than the surface refractive index n_(s)of the CS substrate 10 glass by amounts Δn=n_(f)−n_(s) in the range from0.02 to 0.06 is found to produce adequate measurement results for boththe EPCS and LSP measurements. When S_(n)<0.0004, it is preferred thatΔn be in the high end of the above-stated range, e.g. from 0.05 to 0.06.

In one aspect of the invention, the measurement wavelength λ_(A) for theEPCS measurement is reduced to reduce the normalized slope S_(n) to morereadily satisfy the above-described conditions. In one example, themeasurement wavelength λ_(A) of the EPCS measurement is shorter than themeasurement wavelength λ_(B) Of the LSP measurement by 5% or more, tohelp achieve a smaller normalized slope Sn. In an example, one or morelight blocks (not shown) can be selectively positioned on the beam pathof the EPCS sub-system 100 to preferentially block light rayspropagating at larger incidence angle corresponding to higher effectiveindices. This enhances the contrast of the captured TM and TE fringes ofthe guided modes for the near-surface spike region R1 of the NSWG 18.

In another embodiment, the surface spike region R1 may have normalizedslope S_(n)>0.0005. In an example, the index-matching fluid may beselected to have at the EPCS measurement wavelength λ_(B) a refractiveindex n_(f) very close to the effective refractive index at the zlocation z_(k) at the knee KN, i.e., at the bottom of the spike regionR1. In this case, n_(f)=n_(crit), where n_(crit) is the refractive indexassociated with the critical angle of the spike region, i.e., the anglebelow which light does not travel as a guided wave within the spikeregion R1

In many cases of practical interest, the difference in effective indexbetween the TM and the TE guided wave at the location corresponding tothe bottom of the surface spike region R1 is relatively small. Forexample, in most cases of practical interest the difference is less than0.0006 refractive-index units (RIU), and most often it is between0.00015 and 0.0005 RIU. In an example,

0.0001≤|n _(crit) ^(TM) −n _(crit) ^(TE)|≤0.0006.

In some examples, it is adequate to specify that n_(f)=n_(crit), meaningthat n_(oil)≈n_(crit) ^(TM) and/or n_(oil)≈n_(crit) ^(TE). To be morespecific, n_(f) is not substantially smaller than the smaller of the TMand TE critical indices, and would also not be significantly greaterthan the largest of the TM and TE critical index. Thus, in an example(and to express the above mathematically):

min(n _(crit) ^(TM) ,n _(crit) ^(TE))−0.001≤n _(oil)≤max(n _(crit) ^(TM),n _(crit) ^(TE))+0.001

The upper limit in the equation immediately above is defined to reducethe chances of missing a fringe associated with the spike region R1 bymaking n_(f) greater than the effective index of that fringe when theindex-matching fluid is absent. Thus, to enable proper accounting forall modes for the purposes of accurately calculating of the depth of thesurface spike region R1 (which in an example is defined by a potassiumIOX process), it is preferred that n_(f) be not significantly greaterthan the larger of the TM and TE critical indices n_(knee) ^(TM),n_(knee) ^(TE), but also ideally not significantly greater than thesmaller of the two critical indices.

In one embodiment, the mode fringes in the TM and TE mode spectraassociated with the spike region R1 are spaced far apart in effectiveindex space, e.g., by more than 0.0015 RIU or preferably by more than0.002 RIU or even more preferably by than 0.0025 RIU when there issignificant effective-index difference between the effective index ofthe last fringe in a specific polarization state (TM or TE), and thecorresponding critical index (n_(crit) ^(TM) or n_(crit) ^(TE)). In thisembodiment, the index-matching fluid refractive index n_(oil) may bechosen closer to the higher of the two critical indices, and possiblyhigher than the greater one of them:

max(n _(knee) ^(TM) ,n _(knee) ^(TE))−0.0005≤n _(oil)≤max(n _(knee)^(TM) ,n _(knee) ^(TE))+0.001

or

max(n _(knee) ^(TM) ,n _(knee) ^(TE))−0.0005≤n _(oil)≤max(n _(knee)^(TM) ,n _(knee) ^(TE))+0.0005

These differences in effective index are easy to establish using theEPCS sub-system 100 by measuring the difference in locations of thecritical angles, which correspond to the intensity transitions 166TM and166TE from bright total-internal reflection to dark (partial reflection)on the sensor, and/or fringe positions, and taking into account thecalibration of the instrument (angle per RIU, or pixels per RIU, orspacing of points on the sensor plane per RIU).

In another embodiment having a more general application, the refractiveindex n_(oil) of the index-matching fluid is chosen closer to the lowerof the TM and TE effective indices. This enables the capture of TM andTE fringes that may be close in effective index to the critical index,but may require relatively close proximity between the coupling surface45A of the EPCS coupling prism 42A and the top surface 12 of the CSsubstrate 10 (e.g., a few wavelengths).

More specifically, in this embodiment it is preferred that

min(n _(crit) ^(TM) ,n _(crit) ^(TE))−0.001≤n _(oil)≤max(n _(crit) ^(TM),n _(crit) ^(TE))

or

min(n _(crit) ^(TM) ,n _(crit) ^(TE))−0.001≤n _(oil)≤min(n _(crit) ^(TM),n _(crit) ^(TE))+0.0005.

Furthermore, to reduce significant change in the shape of thecritical-angle transition, it may be preferred that

min(n _(crit) ^(TM) ,n _(crit) ^(TE))−0.0005≤n _(oil)≤min(n _(crit)^(TM) ,n _(crit) ^(TE))+0.0005

or even that

min(n _(crit) ^(TM) ,n _(crit) ^(TE))−0.0002≤n _(oil)

In some cases of practical interest, the guided mode having the lowesteffective index has its effective index very close to that of thecritical index, within about 0.0002 RIU. In this case, it may be idealto also impose a stricter requirement for the index-matching fluidrefractive index to be limited from above:

n _(oil)≤min(n _(crit) ^(TM) ,n _(crit) ^(TE))+0.0002

In cases where n_(oil) is smaller than at least one of the two criticalindices, obtaining a high-contrast transition for proper measurement ofthe critical index n_(crit) may require the aforementioned closeproximity between the coupling surface 45A of the EPCS coupling prism42A and the top surface 12 of the CS substrate 10 (e.g., a fewwavelengths). In an example, this close proximity is enabled by use of avacuum system attracting the specimen toward the prism via the PVconduits 90 pneumatically connected to the vacuum source 92.

In another embodiment, a correction is made for a systematic error inthe calculation of surface compressive stress S(0)=CS when theindex-matching fluid refractive index n_(oil) is not significantlydifferent from the effective indices of the guided optical modes thatare used to calculate the surface compressive stress CS. In particular,such correction may be preferable to utilize when:

min(n _(crit) ^(TM) ,n _(crit) ^(TE))−0.01≤n _(oil)≤max(n _(crit) ^(TM),n _(crit) ^(TE))+0.01

In one example embodiment, the correction is prescribed by calibratingthe systematic error, e.g., by comparison of the surface compressivestress CS measured using the preferred inventive dual-use index-matchingfluid with the CS measured by using a more convention index matchingfluid having a relatively large refractive index n_(oil), such as an oilwith n_(oil)=1.72 at λ_(A)=590 nm used for measuring a CS substrate 10having a bulk refractive index n_(B) in the range 1.45 to 1.55.

In a related embodiment, the systematic error may also be calibratedagainst the breadth of the TM and TE fringes 163TM and 163TE, as thebreadth may be associated with the thickness of the index-matchingfluid, and at the same time associated with the amount of systematicerror in the measurement of the surface compressive stress CS. It shouldbe noted that the systematic error would also depend on the index slopeS_(n) of the refractive index profile of the surface spike region R1 ofthe CS substrate 10. This means that the systematic error can be definedfor a particular type of CS substrate having a surface index slope S_(n)that falls within a relatively narrow range. Such a narrow range istypical for CS substrates that employ Li-based glass that has beenstrengthened using an IOX process.

Hybrid System Employing Two Different Index-Matching Fluids

An example embodiment of the hybrid system 20 employs two differentindex-matching fluids 5 (denoted 5A and 5B) for the EPCS and LSPsub-systems 100 and 200 respectively, with the two differentindex-matching fluids 5A and 5B having respective refractive indicesn_(fA) and n_(fB) (or n_(oil-A) and n_(oil-B)).

Employing two different index-matching fluids 5A and 5B calls forkeeping the two index-matching fluids separated so that they do not mixwith each other. In one example discussed above in connection with FIGS.5A and 5B, the prism support structure 46 includes an isolation member50 disposed between the EPCS coupling prism 42A and the LSP couplingprism 42B to keep the two index-matching fluids 5A and 5B fluidlyseparated, i.e., in fluid isolation from one another.

In another embodiment, a pressurized gas (e.g., air) is introduced intoa small gap between the EPCS coupling prism 42A and the LSP couplingprism 42B to define an “air curtain” 30 (see FIG. 2B) that ensures thatthe index-matching fluids 5A and 5B do not interact with other while theCS substrate 10 is being measured in the hybrid system 20. Thisseparation will then enable automatic dripping of the respectiveindex-matching fluids 5A and 5B onto their respective EPCS and LSPcoupling prisms 42A and 42B at the same time, thus allowing simultaneousmeasurements. In an example, the air curtain 30 can be formed using thevacuum system 91 (see e.g., FIG. 8B).

Hybrid System with Reduced Cross-Talk

Given the proximity of the EPCS coupling prism 42A and the LSP couplingprism 42B, cross-talk between the EPCS sub-system 100 and the LSPsub-system 200 can occur. Such cross-talk can reduce the accuracy of thestress measurement of each sub-system. The various embodiments forreducing (including eliminating) cross-talk described below can be usedseparately or in combination.

In one example, the EPCS detector system 140 for the EPCS sub-system 100includes the aforementioned band-pass filter 144 centered on the EPCSmeasurement wavelength λ_(A). Meanwhile, the LSP detector system 240 forthe LSP sub-system 200 includes a band-pass filter 244 centered on theLSP measurement wavelength λ_(B). In an example, the respectivebandwidths of the band-pass filters 144 and 244 are sufficiently narrowto substantially filter out the other sub-systems measurementwavelength. Since band pass filters can be made very narrow, (e.g., afew nanometers), just a small difference in the measurement wavelengths(e.g., 10 nm) would be more than sufficient to reduce or eliminatecross-talk using the band pass filters. In an example, the given bandpass filter can be inserted anywhere between the corresponding couplingprism and detector system.

In another embodiment, a barrier that is optically opaque to themeasurement EPCS and LSP wavelengths λ_(A) and λ_(B) is disposed betweenthe EPCS coupling prism 42A and the LSP coupling prism 42B. In anexample, the barrier takes the form of the isolation member 50 asdiscussed above in connection with FIG. 5A. The isolation member 50 canbe formed of a rigid material such as aluminum, or a non-rigid materialsuch as rubber, as long as it is capable of stopping EPCS and LSPmeasurement light from communicating between the EPCS and LSP couplingprisms. As noted above, the isolation member 50 can also be configuredto serve the dual purpose of optical isolation and fluid isolation.

Coupling Prism Alignment

The hybrid system 20 provides the most accurate measurements when theEPCS and LSP coupling prisms 42A and 42B are aligned with respect toeach other and with their coupling surfaces 45A and 45B residing in acommon plane.

To achieve such alignment, the coupling prism assembly 40 employs theaforementioned prism support structure 46 is used. In an example offorming the prism support structure 46, the coupling surfaces 45A and45B of the EPCS and LSP coupling prisms 42A and 42B are first ground andpolished to a high degree of flatness and perpendicularity. Withreference again to FIG. 6A, the EPCS and LSP coupling prisms 42A and 42Bare then placed on a stable platform 75, such as a precision flatgranite bar, with the coupling surfaces 45A and 45B resting upon asurface 76 of the stable platform.

With reference now to FIG. 6B, a mold 49 is installed on the stableplatform 75 at the surface 76 and a resin 49R is then poured into themold. Upon hardening of the resin, the walls of the mold 49 are removedto define the prism support structure 46 of the coupling prism assembly40, such as shown in FIG. 5B. In an example, the molded prism supportstructure 46 includes the isolation member 50 in the form of a thin wall47 between the EPCS and LSP coupling prisms 42A and 42B, as shown inFIG. 6C. In an example, the molded prism support structure 46 is formedsuch that at least one of the prisms is partially encased to avoidcross-talk. In an example, the molded prism support structure 46comprises or consists of a unitary molded structure, i.e., is a singlepiece made of a single material (i.e., the piece monolithic) and so isnot formed by joining two or more components.

In an example, the molded prism support structure 46 includes securingtabs 52 that include mounting holes 53 for securing the prism supportstructure 46 to the support plenum 70 (see also FIG. 5A). The use of themovable substrate holder 80 as shown in FIG. 7 and described aboveenables EPCS and LSP measurements to be made at the same location on theCS substrate 10. The movable substrate holder 80 can be moved under theoperation of the system controller 400 by using precision linear motors(e.g., piezoelectric actuators) to set the measurement location for theEPCS and LSP sub-systems 100 and 200.

In an example, the prism support structure 46 includes sections that aremovable with respect to one another so that the EPCS and LSP couplingprisms 42A and 42B can be moved relative to one another, e.g., axiallyor the z-direction as shown in FIG. 6C. In an example, the support frame48 of the prism support structure includes adjacent walls configured sothat one wall can slide relative to the other in a controlled manner. Inthe example of FIG. 6C, the EPCS coupling prism 42A is shown has havingmoved in the z-direction relative to the LSP coupling prism 42B.

FIG. 6D is similar to FIG. 4C and illustrates an embodiment of thehybrid system 20 wherein the EPCS sub-system 100 and the LSP sub-system200 share a common coupling prism 42, i.e., the common coupling prism 42acts as both the EPCS coupling prism 42A and the LSP coupling prism 42B.A single index-matching fluid 5 is also used. The various surfaces ofthe common coupling prism 42 have dual purposes, e.g., the couplingsurface is denoted 45A and 45B because it serves the dual purpose ofperforming EPCS coupling and LSP coupling. In an example, the band-passfilters 144 and 244 of the EPCS sub-system 100 and the LSP sub-system200 are used, along with different wavelengths λ_(A) and λ_(B) (e.g.,separated in wavelength by at least the bandwidth of one of theband-pass filters 144 and 244) to substantially reduce or eliminatecross-talk between the sub-systems. In the example of the commoncoupling prism 42, the coupling prism can have an ECSP section PS1 and aLSP section PS2, and further in the example the sections can beseparate, i.e., the EPCS light beam 116 and the LSP light beam 216generally stay in their respective sections, with the exception of smallamounts of scattered light.

Reducing Substrate Warp

The CS substrate 10 can be large enough that it can warp to the pointwhere making accurate EPCS and LSP stress measurements becomesproblematic. In particular, a warped CS substrate 10 can make itdifficult to establishing the EPCS and LSP coupling interfaces INT1 andINT2 needed for making the EPCS and LSP measurements.

With reference again to FIGS. 8A and 8B, the vacuum system 91 is used toreduce or eliminate substrate warp. The PV conduits (PV bars) 90 are inpneumatic communication with the top surface 12 of the CS substrate 10through the measurement aperture 72 in the support plenum 70, whichsupports the CS substrate so that the top surface 12 residessubstantially at the measurement plane MP. Activation of the vacuumsource 92 generates reduced pressure near the coupling prism assembly 40via the PV conduits 90, resulting in a downward force FD on the CSsubstrate by the surrounding high pressure, as shown by the two largearrows. The PV conduits 90 enable height control of the CS substraterelative to the top surface 71 of the support plenum 70 (and thus to themeasurement plane MP) to within an accuracy of ±5 microns. The use ofthe vacuum system 91 also reduces vibrations and enables non-contactcontrol of the CS substrate for dynamic processing and inspectionwithout the need to stabilize the CS substrate on a vacuum chuck.

The PV conduits 90 are commercially available and can be configured forreducing warp as shown in FIGS. 8A and 8B. Some of the PV conduits 90proximate to the coupling prism assembly 40 may need to be omitted toavoid interference with the EPCS and LSP light beams 116 and 216 andvarious components of the EPCS and LSP sub-systems 100 and 200 thatreside immediately below the support plenum 70. In an example, one ormore stop members 94 can be used to hold the CS substrate 10 in place onthe support plenum 70.

In some cases, it may be desirable that at least one of the EPCS and LSPcoupling prisms 42A and 42B be capable of being adjusted independent ofthe other. In this case, the coupling prism assembly 40 can comprise twoseparate prism support structures 46, with one or both of them beingadjustable. In one example, the EPCS coupling prism 42A is adjustable inthe z-direction to optimize the contrast of the TM and TE mode fringesin the mode spectrum. This can be accomplished by using a single-axismicro-positioner operably attached to the prism support structure 46that holds the EPCS coupling prism in a movable configuration.

Processing EPCS and LSP Measurements

FIG. 9 is a schematic diagram of an example user interface 410 asdisplayed by the system controller 400 of the hybrid system 20. The userinterface 410 includes a EPCS section 412A that shows the mode spectrum160 generated by the EPCS sub-system 100 and a LSP section 412B thatshows the digital LSP image 248D generated by the LSP sub-system 200.The software in the system controller 400 is configured to calculatefirst stress characteristics of the CS substrate using the EPCSmeasurements from the EPCS sub-system 100 (i.e., the mode spectrum 160)and calculate second stress characteristics of the CS substrate usingthe LSP measurements from the LSP sub-system 200 (i.e., the digital LSPimage 248D) and then combine the measurements to generate a complete orfull stress characterization of the CS substrate.

Processing LSP Measurements

In an example, the system controller 400 is configured (e.g., withsoftware) to process the LSP image 248 to extract the “second” or LSPstress characteristics obtained from the LSP sub-system 200. Thisincludes digitally characterizing the contour of the LSP image 248 usinga Gaussian blurred Otsu thresholding is performed as part of the contourdetection method to facilitate the calculation of optical retardationvs. depth (OR vs. D).

FIG. 10A is an example representation of the LSP image 248 as shown inthe LSP section 412B of the user interface 410. The detection of the LSPimage 248 by the digital detector 246 forms a digital LSP image 248D,which can be referred to as a raw LSP image or a raw digital LSP image.The LSP section 412B of the user interface also shows a histogram of thescattered light intensities that constitute the digital LSP image 248Das well as some pertinent statistical measurements. In this exampleview, the primary beam entrance into the CS substrate is from the lowerright to the center of the cross. From the center of the cross to theupper right, the digital camera sees a reflection off the air surface ofCS substrate of the side of the beam (see FIG. 11C below) due to totalinternal reflection. From the center of the cross to the lower left, thedirect beam has reflected off the CS substrate air surface and traversesback through the thickness of CS substrate towards the LSP couplingprism. From the center to the upper left, the digital camera views areflection of the reflected beam.

The digital LSP image 248D is largely comprised of very bright pixelsand pixels with little to no exposure. With reference to FIG. 10B, aspart of the contour detection method, a Gaussian blur is applied to theoriginal (raw) digital LSP image 248D (left-side image) to reduce anyresidual noise. The result is a blurred LSP image 248B (right-sideimage). The Gaussian blurring is applied in a manner that does notobscure the optical retardation information encoded in the intensityvariations of the digital LSP image 248D.

With reference now to FIG. 10C, Otsu thresholding is applied to the(Gaussian) blurred LSP image 248B of FIG. 10B to obtain a threshold LSPimage 248T. The Otsu thresholding mechanism uses the image histogram(see FIG. 10A) to select an intensity value below which all pixels areset to zero. The bright section in FIG. 10C represents all pixels withintensity above that threshold value.

FIG. 10D shows the next process step, which involves using the thresholdLSP image 248T to define an LSP image contour 248C using a binarizingmethod, such as by the application of the known open-source binarizingalgorithm, such as available from open-source image-processingalgorithms (e.g., via OpenCV). The example uses an image coordinatesystem with 0.0 in the upper left and with increasing values to theright (x) direction and down (y) direction. The LSP image contour 248Cis comprised of an array of points that can be split into quadrants tofind the following five critical points of the cross-shaped image: UpperLeft, Upper Right, Lower Left, Lower Right, and Center. The close-up ofFIG. 10D shows an example of the lower left point detection, which isobtained by finding the lowest X and highest Y values in that area. Thesame process is repeated for all four corners, and the center isdetermined by averaging the corner X and Y values.

FIG. 10E shows the final LSP image contour 248C with a fully definedcontour and processed area. In an example, the lower-right leg of theprocessed “X” LSP image contour 248C (see trapezoidal area) is then usedfor calculating the LSP stress characteristics. Horizontal lines in theLSP image contour 248C in FIG. 10E are at constant depth. The intensity(e.g. sum, peak, or average) Gaussian blur across the horizontal linefrom each of the images acquired while the polarization of the lightsource is being modulated, is used as an input for subsequent analysisto obtain the OR vs. D data.

Thus, the threshold LSP image 248T and the LSP image contour 248C areused to define a “mask” that identifies a portion or portions of thecaptured or Gaussian-blurred LSP image 248B to be used for calculatingthe optical retardation OR as a function of depth (D) into the CSsubstrate 10, as explained above.

CS Substrate Thickness Extraction and Beam Angle Calculation

FIG. 11A is a view of the CS substrate 10. FIG. 11A also shows beam pathof a portion of the focused LSP light beam 216F inside the body 11 ofthe CS substrate 10 after going through the LSP coupling prism 42B (notshown). FIG. 11B is a close-up view showing an edge portion of the CSsubstrate 10 as the area of interest for calculating the CS substratethickness TH. FIGS. 11C through 11E are additional views of the path ofthe focused LSP light beam 216F within the CS substrate. The LSPcoupling prism 42B is not shown for ease of illustration.

By looking at the edge of the CS substrate 10 along the direction ofpropagation of the focused LSP light beam 216F, the thickness of the CSsubstrate 10 as seen by the digital detector 246 of the LSP detectorsystem 240 can be highlighted, as shown in FIG. 11B. Since the digitaldetector 246 is looking at the focused LSP light beam 216F through anangled LSP coupling prism 42B (e.g., angled at 45°), the real thicknessTH of the CS substrate 10 can be calculated as

TH=x/{Cos(45°)

where x represents the path length in the plane of the digital detector246.

Once the thickness TH is calculated, the propagation angle A of thefocused LSP light beam 216F within the CS substrate (see FIG. 11E) canbe determined by looking at the edge of the CS substrate 10 along thedirection of the digital detector 246, and using the schematic diagramof FIG. 11E, determining the propagation angle A using:

A=ArcTan(W/TH)

where W is the horizontal distance between the center cross C of the LSPimage contour 248C and the lower right (LR) critical point of the imagecontour as obtained from the contour detection method described above.Once the processed area is selected, the digital detector 246 recordsseveral LSP images 248 as a function of input polarization. The opticalretardation information as a function of depth into the CS substrate isthen extracted using techniques known in the art.

Lock-In Detection Method

The lock-in detection method is a signal analysis technique that hasproven very adept and fast at retrieving a signal that is obscured withnoise. For this method to work, the period of the signal must be known.

The measurement (detector) signal SB from the LSP sub-system 200 has aperiod that depends on the rate of polarization rotation by the opticalcompensator 230. When using a rotating half-wave plate 234RH in theoptical compensator 230, one full rotation corresponds to fouroscillations of the polarization state of the scattered LSP light beam216S.

The derivation of the lock-in method as applied to the LSP measurementsignal SB=s(t) is as follows, where t is time. Consider the LSPmeasurement signal s(t) to be centered around zero and having an amountof noise (“noise factor”) N. The measurement data D(t) received by thesystem controller 400 can be represented as:

D(t)=s(t)+N

The measurement signal s(t) can be generalized in the form

s(t)=A cos(ft+φ)

where φ is the phase value to be extracted and f is the known frequencyof the signal. This signal can be “locked” into by multiplying it with ageneric test wave of an equal and negative period (and arbitrary phase)W(t)=cos (−f−θ) to yield the following equations:

${{D(t)}*{W(t)}} = {{\left( {{A\cos\left( {{ft} + \varphi} \right)} + N} \right)*\left( {\cos\left( {{- {ft}} - \theta} \right)} \right)} = {{\left( {A{}\cos\left( {{ft} + \varphi} \right)*\cos\left( {{- {ft}} - \theta} \right)} \right) + \left( {N*\cos\left( {{- {ft}} - \theta} \right)} \right)} = {{\frac{1}{2}\left( {{A\cos\left( {\phi - \theta} \right)} + {A\cos\left( {{2{ft}} + \varphi + \theta} \right)}} \right)} + {N\cos\left( {{- {ft}} - \theta} \right)}}}}$${{D(t)}*{W(t)}} = {\left( {{\frac{A}{2}\cos\left( {{2{ft}} + \varphi + \theta} \right)} + {N\cos\left( {{- {ft}} - \theta} \right)}} \right) + {\frac{A}{2}\cos{\left( {\phi - \theta} \right).}}}$

The first two terms of the equation for D(t)*W(t) immediately aboveoscillate according to the time variable t. The final term, however, isa constant that can be extracted through strong low-pass filtering ofthe product wave. Since the average of a wave approaches the offsetvalue of that wave over multiple oscillations, this is achieved byaveraging the product wave.

This approximation incurs a slight amount of error if the measurementsignal s(t) does not have many oscillations (e.g. less than one fulloscillation) or if the signal has a non-integer number of half-cycles.This error can be reduced by taking the average of the signal over onlythe largest amount of half-cycles in the signal. For example, if thesignal has about 3.7 oscillations, then take the average of the signalup to 3.5 cycles.

Once the low-pass filtering is performed using known means, the productD(t)*W(t) is reduced to the constant term [A/2] cos(−θ+φ). Recall that φis the desired phase value, and θ is the arbitrary phase of the testwave. Hence, if θ is incremented through a series of numbers, theconstants resulting from the low-pass filtering of the product wave foreach increment will oscillate according to the non-time-varying cosinefunction [A/2] cos(−θ+φ). This cosine wave has a wave number of −1, anamplitude of A/2, and a phase of φ. Knowing this, a cosine can be fit tothese constants (e.g., using least-squares fitting), and the phase φ canbe extracted. The amplitude of the signal A can also be extracted.

The lock-in method for signal extraction has proven to be much fasterthan a regular sine fitting. FIG. 12A is a plot of the averagecomputation time T in milliseconds (ms) needed to extract the phase φ ofa noisy signal versus the noise factor N for both the lock-in method (Lor black curve) and the sine method (S or gray curve). The data for FIG.12A were collected over a series of tests. In these tests, random noisewas added to a set signal upon which both the sine fitting and thelock-in detection methods were used to extract the phase. At each noiselevel 100 tests were performed with randomized noise. The lock-in methodperformed the calculation in approximately half the time that it tookthe sine fitting method.

FIG. 12B is a plot of the absolute phase difference |Δφ| for versus thenoise factor N for the lock-in method (L or black curve) and the sinemethod (S or gray curve). FIG. 12B shows that both methods retainedapproximately the same level of accuracy and precision over all thetests

The lock-in method removes the necessity of predicting the sineparameters for fitting. The only fitting performed is that of the cosinewave to the low-pass filtering constants, which is so constrained thatit almost never produces a bad fit. If sine fitting is used, however, ithas been found that it performs much more accurately when the sine wavethat is fitted to the data has a constant period. If the period can befitted along with the other parameters, the processing time takes longerand the results are often not as accurate.

Noise Reduction in the LSP Measurement

The extraction of second stress characteristics using the LSPmeasurements from the LSP sub-system 200 consists of two main parts—adata acquisition part and data analysis part. In the data acquisitionpart of the measurement, the scattered LSP light beam 216S is imaged asa function of the input polarization state of the initial LSP light beam216 from the LSP light source 212. The imaging is achieved by recordingat the digital detector 246 the intensity of scattered light fromstress-induced features (e.g., refractive index variations) within thebody of the CS substrate 10 due to the IOX process or processes.

The recorded LSP images 248 are processed by the system controller 400to extract the intensity along the laser beam, which is analyzed againstthe input polarization to extract the amount of optical retardationbetween two orthogonal states of the light beam. The stress profile isreconstructed by modeling the observed retardation. As a result, thequality of LSP measured stress profile is fundamentally limited by thenoise in the imaging process, which is typically dominated bylaser-based noise. One example of such laser-based noise is speckle,which originates from the high degree of coherence of the LSP lightsource 212, and imperfections in the optical surfaces (roughness,flatness, etc.) and volume properties of the optical elements(impurities, inhomogeneity and heterogeneity of density, etc.).

During propagation of the LSP light beam 216 through the LSP sub-system200, interactions of the LSP light (laser) beam 216 with systemimperfections result in random amplitude and phase variations within thelight beam wavefront. When the LSP light beam 216 is coherently imagedby Rayleigh scattering, wavefront distortions lead to a staticinterference pattern in the image plane that is called a specklepattern, which is characterized by large intensity variations with highspatial frequencies superimposed on the desired signals. Intensitydeviations from the desired signals are considered as noise in an LSPmeasurement. To reduce the effect of laser speckle, the imaging can beaveraged over independent speckle patterns by modulation ofpolarization, amplitude or phase in the beam wavefront.

In one embodiment, laser-based noise is reduced in the LSP sub-system200 by passing the initial LSP light (laser) beam 216 through a movablelight diffuser 222, which in an example can comprise a holographicdiffuser. This “stirs” the light beam rays within the diffusing angledepending on the local structure of the diffuser. To minimize the beamdivergence caused by this “ray stirring,” the movable light diffuser 222is placed in the image plane of a Keplerian telescope configuration, asshown in the example configuration of FIG. 4A. The LSP light beam 216 isfirst focused onto the movable light diffuser 222 by the first focusinglens 220 and the transmitted light beam is re-collimated by the secondfocusing lens 224.

Mitigating the divergence of the LSP light beam 216 after undergoinglight diffusion provides more efficient (i.e., less aberrated) focusedLSP light beam 216F at the CS substrate. Using the movable lightdiffuser 222, variations the laser-based noise (e.g., speckle pattern)at the digital detector 246 are produced at the rotational velocityv_(D) of the spinning diffuser. The maximal effect of noise averaging isachieved at the v_(D)τ_(C)>1 condition, where τ_(C) is the exposure timeof the digital detector 246. This condition also eliminates a potentialblinking in the imaging caused by optical transmission variations acrossthe movable light diffuser 222. Implementation of diffuser-based noisereduction improves the measurement of the optical retardation. This isillustrated in FIGS. 13A and 13B, which are plots of optical retardationOR (radians) versus depth D (mm) into the CS substrate. The plot of 13Awas obtained without using the noise reduction apparatus and methodsdescribed above. The plot of FIG. 13B was obtained by using the noisereduction apparatus and methods described above. The smoothness of theplot of FIG. 13B is a direct result of the application of thenoise-reducing apparatus and methods disclosed herein.

Shifting the OR Plot Using the Bend Points and CS Substrate Mid-Plane

Since the location of the top surface 12 of the CS substrate 10 can bedifficult to determine from the LSP images 248, the stress profile canbe shifted into position based on the general shape of the retardationcurve (OR vs D). The OR retardation curve has two bend points where thederivative is zero. An example actual OR vs. D curve is shown in FIG.14A along with the two bend points BP1 and BP2. The data points areshown as open circles. The two bend points correspond to where thestress profile changes from compression to tension, or vice versa.

If the stress profile is symmetric, then the two bend points BP1 and BP2should also be symmetric around the mid-plane MP of the CS substrate(see FIG. 1A). Therefore, if the thickness TH of the CS substrate 10 isknown and the two bend points BP1 and BP2 of the optical retardation ORcurve can be found, then the OR profile can be horizontally shifted intothe correct position. This allows for the depth of compression DOC to bemore accurately determined because the location of the top surface 12 ofthe CS substrate 10 is chosen based on the known symmetry and thicknessof the CS substrate. FIG. 14B is similar to FIG. 14A but shows the ORcurve shifted to the left as compared to FIG. 14A using theplot-shifting (data-shifting) technique described above.

Shifting the OR Plot Using Curve Fitting

An alternate method of extracting the DOC for a symmetric stress profileinvolves analyzing the shape of the retardation profile, i.e., the ORvs. D curve. If the thickness TH of the CS substrate is known and therelative positions of the bend points BP1 and BP2 can be determinedthrough polynomial fittings, then the depth of compression DOC of the CSsubstrate can be determined by expression:

DOC=[TH−(BP2−BP1)]/2

where BP1 and BP2 are the relative depth positions of the bend points.

Curve Fitting for the OR Vs. D Curve

An embodiment of the disclosure is directed to methods obtaining anexcellent fit to the data of the OR vs D curve. The methods includeemploying a combination of linear and quadratic functions to obtain thecurve fit. This method is referred to below as the LinQuad method.

FIG. 15A is a plot of OR vs. D data (circles) and shows an examplefitted curve FC (solid line) to the OR data using the LinQuad method.The LinQuad method assumes the following model stress function, where ais the stress, x is the depth coordinate into the CS substrate 10 and Ris as defined below:

${\sigma(x)} = {\frac{d\sigma}{dC}\left( {{C(x)} - {R*C_{0}}} \right)}$

One can extract the corresponding retardation and fit it to the raw dataof interest to recreate the stress profile. Here, C represent thenormalized modeling concentration of ions in the CS substrate. Theirexpressions are as follows.

$\begin{matrix}{{C(x)} = \left\{ \begin{matrix}{C_{0}\left( {1 - \frac{2x}{d_{c} + d_{l}}} \right)} & {{{for}0} \leq x \leq d_{l}} \\{C_{0}\left( {1 - \frac{2d_{l}}{d_{c} + d_{l}}} \right)\frac{\left( {d_{c} - x} \right)^{2}}{\left( {d_{c} - d_{l}} \right)^{2}}} & {{{for}d_{l}} \leq x \leq d_{c}} \\{{0{for}x} \geq d_{c}} & \end{matrix} \right.} & \end{matrix}$$\ {{R = {\frac{2}{3}\frac{d_{c}}{t}\frac{1 + \delta + \delta^{2}}{1 + \delta}}},{\delta = \frac{d_{l}}{d_{c}}}}$

where d_(l) is the depth of the linear region, d_(c) is the depth of thecurved region, C₀ is a constant multiplier and t is the CS substratethickness.

An alternate expression is given by:

${\sigma(x)} = {{CT} - {{C(x)}*\frac{d\sigma}{dC}}}$

Here, CT is the central tension of the stress profile, and

$\frac{d\sigma}{dC}$

is a (partially arbitrary) constant of around

$60{\frac{MPa}{{mol}\%}.}$

The true LinQuad function is defined above, where only d_(c), d_(l), C₀are fit. However, this latest expression for σ(x) allows a fourthparameter—namely the central tension CT—to vary, which can help thefunction fit the data more closely.

FIG. 15B is a plot of the stress S(x)=σ(x) versus depth D (mm) (or xcoordinate) based on the LinQuad fit to the OR vs. D curve of FIG. 14A.

Power-Spike Function

A power-spike function is defined as:

${{{\sigma(x)} = \left. {{CT_{sp}} + {CT_{p}} - {C{T_{p}\left( {p + 1} \right)}*}} \middle| \frac{2\left( {x - {mid}} \right)}{t} \right|^{p}}} - {\left( {{CS}_{sp} - {p*CT_{p}}} \right)*\left( {2 - {{ERF}\left( \frac{x}{L_{{eff},{sp}}} \right)} - {{ERF}\left( \frac{t - x}{L_{{eff},{sp}}} \right)}} \right)}$${CT}_{sp} = {2*\left( {{CS}_{sp} - {p*{CT}_{p}}} \right)*\frac{L_{{eff},{sp}}}{t\sqrt{\pi}}}$${CT}_{sp} = {2*\left( {{CS}_{sp} - {p*{CT}_{p}}} \right)*\frac{L_{{eff},{sp}}}{t\sqrt{\pi}}}$$L_{effsp} = \frac{{DOL}_{sp}}{{1.3}829}$

where CT_(sp) is the central tension of the spike in the spike regionR1, mid is half of the thickness TH, CS_(sp) is the compressive stressof the spike, and DOL_(sp) is the depth of layer for the spike. Theparameter L_(eff) is an effective length (depth) of the spike region R1.This function is a stitching of a power profile with two error functionspikes at the ends. The CS_(sp) and DOL_(sp) values are specific to eachglass type and are entered as a constant. The only parameters that needto be fitted are the power of the function p and the peak centraltension CT_(p).

FIG. 16A is a OR vs. D plot illustrating an example fitted curve FCusing the power-spike function. FIG. 16B is plot of the stress profileS(x) (MPa) versus depth D into the CS substrate 10 based the power-spikefunction fit to the OR vs. D curve of FIG. 16A.

Removing Systematic Error to Conform with a Symmetric Stress Profile

The stress profile of the CS substrate using the LSP measurement data isobtained by differentiating the OR vs. D curve. As such, a symmetricstress profile will always correspond to an asymmetric OR vs. D curve.However, systematic error from various components in the LSP sub-system200 can introduce a symmetric component into the OR vs. D retardationdata, thereby hindering the accurate extraction of the stress profile.This effect can be mitigated by decomposing the retardation data intosymmetric and anti-symmetric components, and only fitting theanti-symmetric portion (i.e., the asymmetric data points).

Given a optical retardation OR in the form of a function ƒ(x), thedecomposition can be achieved as follows.

ƒ(x)=ƒ_(s)(x)+ƒ_(a)(x)

where ƒ_(s) and ƒ_(a) are the symmetric and anti-symmetric components ofthe retardation ƒ, and expressed by the following equations:

${f_{s}(x)} = \frac{{f(x)} + {f\left( {- x} \right)}}{2}$${f_{a}(x)} = \frac{{f(x)} - {f\left( {- x} \right)}}{2}$

FIG. 17A is fit to the OR vs. D plot based on the original OR data whileFIG. 17B is a fit to the OR vs. D plot with the symmetric component ofthe data removed using the technique described above. The fitting errorof the fitted curve FC to the measurement data in FIG. 17B is 0.006while that of FIG. 17A is about 0.46

Adjustable Fitting Regions for Accurate CT and DOC

A single fit to the OR v. D curve may not always be adequate toaccurately determine both the central tension CT and the depth ofcompression DOC. This is because scattering from the LSP coupling prism42B or the coupling interface INT2 can hinder data collection close tothe top surface 12 of the CS substrate 10.

In an example, the fit to the OR vs. D curve is performed using fits toseparate regions of the curve respectively associate with the centraltension CT and depth of compression DOC and adjust the fitting range ofthe OR data for accurate CT and DOC extractions.

FIGS. 18A and 18B show an example OR vs. D curve wherein regions aroundthe bend points BP1 and BP2 defined by the data (circles) are fitted toextract the depth of compression DOC. FIG. 18B shows the central linearregion between the bend points BP1 and BP2 fitted to extract the centraltension CT. In both cases, the range of the OR vs. D data issubstantially reduced to that portion of the OR vs. D curve that isrelevant to the given stress parameter.

FIGS. 19A through 19D further illustrate the effect of data rangeselection (shown by vertical dashed lines) on the fitting quality. FIG.19A is a OR vs. D plot where the full data range is considered and wherethe fitted curve does not fit the bend points BP1 and BP2 very closely.FIG. 19B is the corresponding plot for FIG. 19A of the stress S(x)versus D (depth) that shows the compressive stress CT and the depth ofcompression DOC.

FIG. 19C is an OR vs. D plot similar to FIG. 19A except that the datarange is reduced to the region between the vertical dashed lines and soomits first and second “end regions” ER1 and ER2 of the measurementdata. The fitted curve FC of FIG. 19C closely follows the bend pointsBP1 and BP2. The corresponding S(x) vs. D plot is shown in FIG. 19C andthe values for the compressive stress CT and the depth of compressionDOC differ substantially from that of FIG. 19B in which the full rangeof data was used.

Simultaneous EPCS and LSP Measurement Considerations

One method of achieving good precision for the measurement of the depthof compression (DOC) using the LSP sub-system 200 is to press the CSsubstrate 10 against a stop surface (e.g., the support plenum 70) toensure that the top surface 12 of the CS substrate 10 is co-planar witha pre-defined surface that can be assigned a depth of z=0. This pressingcan be achieved by either pushing the CS substrate 10 against the stop,or by applying a vacuum such that the ambient atmospheric pressureprovides the force to push the top surface 12 of the CS substrate 10into place at z=0 (see e.g., FIGS. 8A, 8B).

On the other hand, achieving sharp (i.e., high contrast) mode spectrum160 using the EPCS sub-system 100 to obtain an accurate stressmeasurement of the near-surface region R1 of the NSWG 18 also usuallyrequires good CS substrate flatness in the EPCS measurement area, whichmay be also achieved with the use of the vacuum system 91.

Due to the EPCS and LSP measurement areas being at different locationsof the CS substrate, applying vacuum at the LSP measurement area can insome case deform the CS substrate at the EPCS measurement area, andresult in sub-optimal, or even very poor flatness or significantlydeformed surface in the EPCS measurement area. This results in an EPCSmode spectrum 160 that has poor contrast and is “out of focus”. Theseconditions can lead to decreased accuracy and decreased precision, aswell as a failure to measure because the poor contrast can cause thesystem controller to fail to identify some of the target features of themode spectrum 160 used to perform the stress calculations.

In an example embodiment, the EPCS detector system 140 of the EPCSsub-system 100 utilizes adaptive focusing to enable proper alignment ofthe CS substrate 10 on the support plenum 70 for the best (most precise)DOC measurement and near-surface stress measurements using the EPCSsub-system when the CS substrate is aligned for a best LSP measurementfor the LSP sub-system 200.

In one embodiment illustrated in FIG. 20, this is accomplished by makingthe focusing lens 142 of the EPCS detector system 140 adjustable, e.g.,axially movable by mounting the focusing lens on a translation stage143, which in an example is operably connected to and controlled by thesystem controller 400. In an example, the translation stage 143comprises a precision linear actuator, such as a piezoelectric actuator.In another example, the translation stage 143 comprises ball screwactuator. This allows for the focusing lens 142 to be translated alongthe second optical axis A2 to improve or maximize the contrast of themode spectrum 160 captured by the EPCS digital detector 150. In anexample, the contrast of the mode spectrum 160 is improved to enhancetarget spectral features, such as the TM and TE fringes 163TM, 163TE andthe critical angle transitions 166TM and 166TE.

The position of the axial movable focusing lens 142 can be monitoredelectronically by the system controller 400 to correct the EPCSsub-system calibration by accounting for the “optical path length” orOPL, e.g., the distance from the focusing lens 142 to the EPCS digitaldetector 150. In one embodiment, the accounting can be simplified aslong as the OPL does not fall outside of a pre-defined acceptable range,so that the original calibration remains accurate. In anotherembodiment, the calibration is corrected based on the OPL, and thesurface stress S(0)=CS and/or the depth of layer DOL is calculated basedon the corrected calibration.

In another embodiment, the focusing lens f1 has variable effective focallength which is actively controlled by the system controller 400 toobtain a high-contrast mode spectrum 160 when the specimen is aligned toensure most precise or accurate measurement of the depth of compressionDOC for the LSP sub-system 200. The variable focal length focusing lens142 can comprise a compound lens (similar to photographicmulti-component lenses with more than one optical element), or maybeotherwise comprise an adaptive lens, such as a fluid-filled lens wherevarying the pressure of the fluid changes the shape of the lens and thusthe focal distance. When using variable focal length focusing lens 142,shifting the position of the focusing lens 142 may not be necessary, aschanging the focal length can in many cases be adequate to compensatefor the deformation of the specimen shape in the EPCS measurement areaas a result of aligning the specimen for best measurement in theLSP-measurement area.

In another embodiment, the variation of effective focal length of thefocusing lens 142 may be enabled by an adaptive lens surface in the formof a mirror surface that may be combined with a fixed simple lens toproduce a net effective focal length that can be varied over a rangesufficient to produce a high-contrast mode spectrum 160 even when the CSsubstrate alignment is optimized for the LSP sub-system 200.

Since the deformation in the CS substrate 10 tends to not be very large,the change in refractive power for the variable focus focusing lens 142need not be particularly large to compensate. In an example, the focallength of the focusing lens 142 can be changed by up to 15%, or inanother example up to 10%.

On the other hand, when the CS substrate 10 has thickness less than 0.6mm, it may be necessary to change the refractive power by more than 15%,and by as much as 20% or even 25%. Thus, in an example, the adaptivesystem for changing the focal length of the focusing lens 142 isconfigured to change the focal length over a focal length range thatrepresents 25% of the average focal length, although in many cases arange of 20%, 15%, or even 10% of the average focal length may beadequate.

Similarly, since for measurements of flat CS substrates, the focusinglens 142 system is focused on infinity, when the focusing lens 142 hasfixed focal length and the position of the focusing lens is axiallyadjusted to produce a high-contrast mode spectrum 160, the range ofaxial positions that are accessible by the focusing lens would ideallyrepresent about 25% of the focal length of the lens, although in somecases 20%, 15%, or even 10% of the focal length may represent anadequate range of positions.

FIGS. 21A and 21B are schematic diagrams of example embodiments whereintwo or more focusing lenses 142 of slightly different focal lengths aremounted on a support member 152 to define a focusing lens assembly 153.The support member 152 is movable to place a select one of the focusinglenses 142 in the optical path (i.e., along the second axis A2) of thereflected EPCS light beam 116R. This allows a user to choose a focallength of the focusing lens 142 from a discrete set of focal lengths.FIG. 21A shows an example where the support member 152 is in the form ofa rotatable wheel that is rotatable about a rotation axis AW. FIG. 21Bshows an example where the support member 152 is in the form of alinearly translatable support frame. Four example focusing lenses 142are shown. In general, the focusing lens assembly 153 can support two ormore focusing lenses 142.

If the contrast of the features of interest (e.g., the TM and TE modelines 163TM, 163TE, the TM and TE critical angle transitions 166TM, 166TE, etc.) in the mode spectrum 160 is deemed adequate, the measurementproceeds as usual. If the contrast of the features of interest is deemedinadequate, then a focusing lens 142 of a different focal length ismoved into the optical path of the reflected EPCS light beam 116R and anew mode spectrum 160 is captured by the EPCS digital detector 150 andthe contrast analyzed. This process repeats until a mode spectrum 160 ofadequate contrast is obtained.

In an example, differences in the focal lengths of the focusing lenses142 may be set by the total desired range of focal-length coverage andthe total number of lenses on the support member. In one example, thereare six focusing lenses supported by the support member, with thefocusing lenses covering a range that is between 20% and 30% of theaverage focal length for the entire set of focusing lenses, and thespacing of focal lengths is between 3% and 7% of the average focallength.

In another example, the focal lengths are spaced unevenly, such that thespacing of each pair of neighboring focal lengths is approximately afixed percentage of the average of the neighboring focal lengths, wherethat percentage is between 2% and 20%, and more preferably between 3%and 10%.

In another related embodiment, some or all of the focusing lenses 142comprise Fresnel lenses. In another embodiment, the focusing lenses 142need not have different focal lengths, but may be positioned on themovable support member in such a way that when the focusing lens ofchoice is placed in the optical path, its distance from the EPCS digitaldetector 150 is different than for the other focusing lenses. In thisembodiment, obtaining a spectrum having adequate contrast for thefeatures of interest is guaranteed not necessarily by having a completeset of discrete densely spaced custom-chosen focal lengths, but by a setof distances to the digital detector and/or available focal lengths.This can reduce the cost of the EPCS sub-system 100 by utilizingstandard off-the-shelf focusing lenses, and positioning each focusinglens to produce a sharp image for a specific range of warp/curvature ofthe CS substrate 10.

In an example, the system controller 400 can be configured to select oneof the focusing lenses 142 based on a measurement of the contrast of thefeatures of interest of the captured mode spectrum 160.

In another embodiment, measurements can be made by using two or threepreferred mode spectra 160 having the best contrast among all capturedmode spectra, and then a preferred result may be calculated as anaverage of the two or three preferred mode spectra. In an example, thepreferred result may be calculated as a weighted average of the two orthree preferred mode spectra. In a related example, the weight for eachpreferred spectrum may be proportional to the contrast of a feature ofinterest the preferred mode spectrum.

Using an Independent Stress Measurement for Stress MeasurementCalibration

The EPCS sub-system 100 can be very good at obtaining a high-contrastmode spectrum 160 for a CS substrate formed an IOX process using aLi-based glass, e.g., wherein K ions replace Li and/or Na ions from theglass in the near-surface region. This in turn allows for very goodmeasurements of the knee stress CS_(k) by measuring the birefringencebased on the relative positions of the TM and TE critical-angletransitions 166TM and 166TE (see FIG. 3B).

On the other hand, the EPCS measurement of the knee stress CS_(k)usually has lower relative precision than the measurement of the surfacestress S(0). In particular, the standard deviation of the measurement ofthe knee stress CS_(k) is usually several % of its average value,whereas the standard deviation of the surface stress S(0) is usually onthe order of 1% to 2% of its average value. In addition, the value ofthe knee stress CS_(k) as obtained simply as a ratio of thebirefringence B of the detected critical angle and the stress-opticcoefficient (SOC) differs slightly from the value of the knee stressCS_(k) as obtained from a destructive RNF measurement of the stressprofile.

When the EPCS measurement of the knee stress CS_(k) is believed to beless accurate than it could be or should be, it can be due to asystematic error in the measurement of the birefringence of the criticalangle. This systematic error can be caused by the TM and TE mode lines163TM and 163TE being too close to the TM and TE critical angletransitions 166TM and 166TE and further by the particular shapes of theTM and TE refractive index profiles.

When making quality-control measurements, such systematic errors aremitigated by calibrating the EPCS-based measurements of the knee stressCS_(k) measurement with corresponding independent reference stressmeasurement, which may be a destructive measurement on a CS substratetaken from a set of CS substrates formed using the identical process orfrom the same batch during the same identical process. In an example,this is accomplished by applying a calibration multiplier K_(cal) basedon the independent measurement via the relationship:

CS _(k)(EPCS,calibrated)=K _(cal) ·CS _(k)(independent).

In an example, the calibration multiplier K_(cal) can be used as ageneral calibration factor for the stress profile calculated by the EPCSsub-system 100 via the equation:

S(EPCS,calibrated)=K _(cal) ·S(original)

where S(orig) is the originally measured (uncalibrated) stress profileS(z).

Tension Zone Stress Profile Extraction

An IOX process used to form a CS substrate 10 forms a compression zonethat defines the NSWG 18. This compression zone extends into thesubstrate and reaches a zero value, which defines the depth ofcompression DOC. Beyond the DOC, the compression zone ends and a tensionzone begins.

If the stress profile in the tension zone can be accurately extracted,it can serve as a powerful tool to help extract a substantially accuraterepresentation of the stress profile in the compression zone. This canbe done by exploiting force-balancing of the stress in the entire CSsubstrate 10 or half of the CS substrate (i.e., so-called “half forcebalancing”).

In one embodiment, besides the area of the stress profile in the tensionzone (which is represented by the depth integral of tensile stress fromone depth of compression to the opposite-side depth of compression), areliable value of the slope of the stress profile at a depth of reliableslope extraction is also obtained from the LSP-based measurement.

In an example, the depth of reliable slope extraction may be the depthof compression DOC. In the compressive-stress region, a surfacecompressive stress is determined by the EPCS method. In some cases, aportion of the compressive-stress profile is also extracted from EPCSmethod using prior-art techniques such as IWKB, or linear-profile,erfc-shaped profile, exponential-profile, or a LinQuad profileapproximation when there are not enough guided modes for reliable IWKBextraction. The EPCS-based method then provides a target point ofconnection, either at the surface with a surface stress value S(0), orat a deeper connection point (for example, the knee depth z_(k); seeFIG. 1B), up to which the surface portion of the stress profile S(z) canbe extracted from EPCS measurement. In the latter case, the knee stressCS_(k) may not be specified with high accuracy due to limitations of theEPCS measurement.

Nonetheless, this value of the knee stress CS_(k) can provide anadequate starting point for pursuing extraction of the stress profile inthe compression zone (e.g., substantially zones R1 and R2 in FIG. 1B) byiterative improvement. In a first iteration, the near-surface connectionpoint with surface stress value S(0) may be connected with a deepconnection point (e.g., the knee stress CS_(k) or the depth ofcompression DOC) with a reliably extracted stress slope using asecond-order polynomial. This determines a first approximation of thestress profile in the compression zone, having a first portion obtainedfrom EPCS up to the first connection point (say, at the knee depthz_(k)) and a second portion obtained via polynomial interpolationbetween the two connection points, where at the second connection pointnot only the surface stress S(0) matched, but also the stress profileslope.

In a particular example, the second connection point can be the depth ofcompression DOC, but it need not be. The first approximation of thestress profile S(z) is integrated. If the stress profile is asymmetric,EPCS measurements may be performed on both sides of the specimen, andfirst approximations of the stress profile obtained as above for eachside. If the stress profile S(z) is symmetric by design andimplementation, then it may be assumed that the back side of thespecimen has the same stress profile in the back-side compression regionas the front-side compression region.

The first approximation of the stress profile from both front-side andback-side compression zones is integrated with respect to depth over therespective compression zones, and compared to the depth integral oftension over the tension zone. If the difference is larger in absolutevalue than a pre-defined acceptable limit, a corrective step isperformed to reduce the difference. In an example, the pre-definedacceptable limit is 5% of the tension-zone stress area, butprogressively better acceptable limits include 3%, 2%, 1%, and 0.5%.

The acceptable limit may be determined based on an estimate of thedegree of accuracy of extraction of the tension-zone stress profile. Inone embodiment, several first approximations for the stress profile areobtained by different methods, all of which match the knee stress CS_(k)at the first connection point, and the stress value and stress slope atthe second connection point, say the depth of compress DOC. Differenttypes of first approximations may include second, third, and 4^(th)order polynomials, an exponential profile, an erfc-shaped profile, aGaussian profile, and a Lorentzian profile. Then, for each of thesefirst approximations, the difference is found between the stress area inthe first-approximation compression zone, and the stress area in thetension zone extracted using LSP-based measurement. Then a linearcombination of these first-approximation stress profiles is found, suchthat the stress area of the linear-combination stress profile equals thetension-zone stress area.

In another embodiment, the limited accuracy of the EPCS-basedmeasurement of the knee stress CS_(k) is taken into account by allowinga range of the knee stress CS_(k) to be targeted around the initialEPCS-based estimate of the knee stress CS_(k). In a first approximationof the compressive-stress portion of the stress profile, the connectionis made with the EPCS-based initial value of the knee stress CS_(k),using a preferred target shape function for the interpolated region ofthe compression zone. In an example, the preferred target shape is asecond-order polynomial.

After each iteration, the stress area of the compressive-stress profilefrom the two combined compression zones (one on each side of thespecimen) is subtracted from the stress area of the tension zone. If thedifference is larger in absolute value than a target pre-definedacceptable limit, then the target value of the knee stress CS_(k) may bechanged within a pre-defined acceptable range for the knee CS_(k) asdetermined in accordance with an estimated precision of the knee stressmeasurement available from the EPCS-based method.

In an example, an estimated knee stress precision is about 10 MPa,though in some cases it is better at 7 MPa or 5 MPa or 3 MPa. When nosurface spike is present, and no guided modes are available, then thesame technique may be used to connect to a target surface stress S(0)that is allowed to vary in a range determined by the precision of thesurface stress measurement.

In an example, the range for acceptable values for the target surfacestress S(0) or knee stress CS_(k) may be up to 6 standard deviationswide, e.g., 3 standard deviations on either side of the measured valueof surface stress or the knee stress. In one embodiment, the targetsurface value S(0) need not be varied iteratively, but may be determinedby algebraic calculation, utilizing the measured difference in areabetween the first-approximation stress profile and the tension-zonestress profile and the preferred functional form chosen for theinterpolated portion of the compressive-stress region.

Enhanced EPCS Sub-System

FIG. 22A is similar to FIG. 3A and illustrates an example of an enhancedEPCS sub-system 100. The enhanced EPCS sub-system 100 places the EPCSlight source 112 at a remote location relative to the EPCS couplingprism 42A. The remote EPCS light source 112 is multiwavelength and caninclude one or more light source elements 123 (e.g., 123 a, 123 b, 123c, . . . ) that respectively emit light of different wavelengths λ_(a),λ_(b), λ_(c), . . . The multiwavelength EPCS light source 112 can alsoinclude a single light source element 123 that emits broadband light,wherein the different wavelengths fall within or at different locationswithin the broadband light spectrum.

The EPCS light source 112 is optically connected to a focusing opticalsystem 121 by a light guide 130 having an input end 131, an output end132 and an axial length AL (see the close-up inset of a stretched outlight guide 130 at the bottom of the Figure). In an example, thefocusing optical system 121 can comprise one or more lens elements. Inan example, the focusing optical system 121 can be color-corrected,i.e., be designed to image multiple wavelengths without substantialchromatic aberrations. This can be accomplished using achromatic lensesand optical coatings designed for the wavelengths or wavelength rangeemployed.

In an example, the light guide 130 can comprise a liquid-filled lightguide, such as is available from ThorLabs, Inc., Newton, N.J., as partnumber LLG5-4T. In another example, the light guide 130 can comprise anoptical fiber bundle or a solid light pipe. An example light guide 130has an axial length AL of at least several inches and preferably 8″ orlonger, with the precise length determined by the location of the remoteEPCS light source 112.

The EPCS light beam (hereinafter, light or light beam) 116 from theremote EPCS light source 112 is coupled into the input end 131 of thelight guide 130 travels therein as guided light 116G. The light couplingcan be facilitated by using one or more lens elements 135 (see FIG. 23).The guided light 116G travels to the output end 132 of the light guide130 and is emitted as the initial EPCS light beam 116. This initial EPCSlight beam 116 emitted from the output end 132 of the light guide 130 isdivergent. This divergent light is received by the focusing opticalsystem 121, which forms there from the focused EPCS light beam 116F,which is directed to the EPCS coupling prism 42A. The rest of theexample EPCS sub-system 100 of FIG. 22A is as described above inconnection with FIG. 3A. The light guide 130, the lens elements 135 andother optional optical components between the light source and the lightguide 130 (e.g., the diffuser 137, introduced and discussed below)constitute a light guide assembly that transfers EPCS light beam 116(either sequentially filtered or multiwavelength) from the EPCS lightsource 112 to the focusing optical system 121 that resides proximate theEPCS coupling prism 42A.

FIG. 22B is similar to FIG. 22A and illustrates an embodiment whereinthe split TM-TE polarizer 148 is replaced by a switchable TM-TEpolarizer 148S. The switchable TM-TE polarizer 148S is controlled by apolarizer controller 149, which is operably connected to the systemcontroller 400. In this configuration, the EPCS digital detector 150sequentially detects a TM mode spectrum 161TM and then a TE modespectrum 161TE for each wavelength rather than detecting a combinedTM-TE mode spectrum 160 for each wavelength (see FIG. 3B) when using thesplit TM-TE polarizer 148 of FIG. 3A. This approach increases the numberof detector pixels available for the mode spectrum images 161TM and161TE and obviates some resolution/contrast issues that occur at theboundary between the combined TM-TE mode spectrum 160 when using thesplit TM-TE polarizer 148. An example switchable TM-TE polarizer 148Scomprises a magnetically charged polarizing crystal as is known in theart of polarization switching. The analysis of the sequentially capturedmode spectrum images 161TM and 161TE is the same as that forsimultaneously captured mode spectrum images using the fixed TM-TEpolarizer 148.

FIG. 23 is a schematic diagram of an example embodiment of the remoteEPCS light source 112. The example remote EPCS light source 112comprises multiple light source elements 123, with three light sourceelements 123 a, 123 b and 123 c shown by way of example. The examplelight source elements 123 a, 123 b and 123 c respectively emit lightbeams 116 a, 116 b and 116 c having the respective wavelengths λ_(a),λ_(b) and λ_(c). The light beams 116 a, 116 b and 116 c are directed totravel along a common light-source axis AS using wavelength-selectiveelements 125 a and 125 b, which in example are dichroic mirrorsrespectively configured to transmit light of one wavelength band whilereflecting light of another wavelength band. In an example, the lightbeams 116 a, 116 b, 116 c combine to form a single multiwavelength EPCSlight beam 116.

In an example, the light source elements 123 are operably connected toand controlled by the system controller 400 or alternatively by alight-source-element (LSE) controller 405 operably connected to thesystem controller 400. The light source elements 123 can be activatedsimultaneously or sequentially as discussed in greater detail below. Thelight source elements 123 need not be narrow band and in an example cancollectively produce light that is relatively broad band to provide arelatively wide range of measurement wavelengths, such as over the rangefrom near UV to near IR.

With continuing reference to FIG. 23, the example light source systemfurther includes an optical filter apparatus 500, such as disclosed inU.S. Provisional Patent Application Ser. No. 63/002,468, filed on Mar.31, 2020, and which is incorporated by reference herein in its entirety.FIG. 24A is a front-on view of a portion of the optical filter apparatus500 referred to as the filter wheel 530. The filter wheel 530 comprisesa support member 510 that operably supports in two or more apertures 516that respectively contain two or more optical filter assemblies 600,which can be denoted 600 a, 600 b, . . . 600 m for an integer number mof optical filter assemblies. The different optical filter assemblies600 a, 600 b, 600 c, 600 d, . . . 600 m each have a filter axis AF andare configured to perform narrow-band optical filtering of the EPCSlight beam 116 at respective wavelengths λ_(a), λ_(b), λ_(c), λ_(d), . .. λ_(m) having respective relatively narrow bandwidths δλ_(a), δλ₄,δλ_(c), δλ_(d), . . . δλ_(m), such as 2 nm for example. The opticalfilter apparatus 500 is thus configured to perform narrow-band opticalfiltering using the optical filter assemblies 600 so that relativelywide band light (e.g., greater than 3 nm or greater than 5 nm, orgreater than 10 nm or greater than 20 nm, etc., and including verybroadband light with a bandwidth of 100 nm or many hundreds of nm) thatincludes a given wavelength can be narrow-band filtered around thatwavelength. In the discussion below, light that has passes through oneof the optical filter assemblies is referred to as filtered light. Thefiltered light is narrow band and has the center wavelength defined bythe filter through which it has passed.

FIG. 24A shows an example filter wheel 530 wherein the support member510 supports four different optical filter assemblies 600 (600 a, 600 b,600 c and 600 d) having respective narrow-band filter (center)wavelengths of λ_(a), λ_(b), λ_(c) and λ_(d). The example support member510 of FIG. 24A has a circular disc-shaped body with a central axis AW,a central section 512 and an outer section 514, with the optical filterassemblies being supported in the outer section, and in an exampleevenly distributed thereover. The support member 510 also has an outerperimeter 523, a front side 522 and a back side (not shown). The centralaxis AW runs through the central section 512 of the circular disc-shapedbody as shown. The combination of the support member 510 and opticalfilter apparatus 500 constitute the filter wheel 530.

With reference again to FIG. 23, a drive system 540 is mechanicallyconnected to the support member 510 and is configured to cause themovement of the support member. An example drive system comprises adrive shaft 544 having one of its ends attached to the central section512 of the support member 510 while its other end is attached to a drivemotor 550. The drive shaft 544 is disposed co-axially with the supportmember axis AW. The drive motor 550 is electrically connected to thesystem controller 400, which is configured (e.g., using controlsoftware) to control the operation of the drive motor 550 using forexample a motor control signal while also receiving a data signal thatincludes information about the motor operation, such as the rotationrate, the relative rotational position of the filter wheel 530, etc.

The drive system 540 causes the filter wheel 530 to rotate about arotation axis AR that is coaxial with the support member axis AW. Thefilter wheel 530 is in turn disposed such that the optical filterapparatus 500 sequentially intersect the light source axis AS so thatthe EPCS light beam 116 is sequentially filtered to form a sequentiallyfiltered EPCS light beam 116 (i.e., one that includes a sequence offiltered light beams 116 a, 116 b, . . . 116 m), as shown downstream ofthe optical filter assembly in FIG. 23 and in the schematic diagram ofFIG. 24B. FIG. 24B shows two exemplary sequentially filtered EPCS lightbeams 116, with the top example formed using four filter wavelengths(116 a, 116 b, 116 c, and 116 d) and the bottom example formed using twofilter wavelengths (116 a and 116 b). The sequentially filtered EPCSlight beam 116 then enters the input end 131 of the light guide 130. Asnoted above, this can be facilitated by using one or more lens elements135 operably disposed along the light source axis AS between the filterwheel 530 and the input end 131 of the light guide 130.

The timing of the activation of the light source elements 123 and theposition of the optical filter assemblies 600 is controlled by thesystem controller 400 so that the appropriate portion of thesequentially filtered EPCS light beam 116 is filtered. Alternatively,all the one or more light source elements 123 can be activated at onceto form a broad-band EPCS light beam 116, with the optical filterapparatus 500 used to sequentially define the filtered light beams 116a, 116 b, . . . 116 m that enter the light guide 130 and are eventuallydirected to the prism assembly 40 as the filtered and focused EPCS lightbeam 116F (see FIG. 22A)

In an example, the optical filter apparatus 500 is focus corrected tocompensate for different focuses of the different wavelength portions ofthe sequentially filtered EPCS light beam 116, with the differentfocuses being due to the different wavelengths. The focus correction canbe accomplished by the use of correction lenses 124 a, 124 b, 124 c, . .. configured (e.g., axially positioned, having different optical powers,etc.) so that the a given one of the sequentially filtered light beams116 a, 116 b, . . . 116 m is efficiently coupled into the input end 131of the light guide 130 for each wavelength of light used. In anotherexample, the focus correction can be employed by each optical filterassembly 600 having a filter 620 and a correcting member 630 configuredfor focus correction at the given filter wavelength, as shown in theclose-up inset in FIG. 23 and as described in detail in theaforementioned U.S. Provisional Patent Application No. 63/002,468.

It is noted that the optical filter apparatus 500 can also be deployedwithin the EPCS detector system 140 to accomplish the same goal ofproviding narrow-band measurement light of different wavelengths so thatthe mode spectrum of the given CS substrate 10 can be measured at eachof a number of different wavelengths in order to improve measurementaccuracy of a stress-related characteristic of the CS substrate.

The illumination provided to the EPCS coupling prism 42A by the EPCSlight source system 110 can be determined by overall system timing andthe wavelengths of interest employed. In one example, the EPCS lightsource 112 can include a single broadband light source element 123, suchas a Halogen bulb, and, incandescent bulb, a xenon bulb or a white-lightLED or laser diode, and rely on the optical filter assemblies 600 forchoosing the wavelengths and band passes. In another example, multiplelight source elements 123 that emit different wavelengths can be used toproduce light at the wavelengths of choice, such as in the mannerdescribed above. In the illustrated embodiment of FIG. 23 that utilizesthree light source elements 123 (123 a, 123 b, 123 c) and twowavelength-selective elements 125, two of the light source elements canrespectively emit short and long wavelengths over relatively narrowbands while and the third has relatively broad band emission at anin-between wavelength. For example, the short wavelength could be 365nm, the long wavelength could be 780 nm, and the broader band wavelengthmight be a human eye white light device comprising a dominant blue (450nm) LED that includes wavelengths of 450 nm, 510 nm and 640 nm. Thesethree light source elements 123 can be activated simultaneously andcontinuously with a simple continuous power supply configuration,relying on the bandpass filter configuration of the optical filterapparatus 500 to only pass the desired (narrow-band) wavelength in asequential manner. Adding control of the beam intensity (e.g., using avariable optical attenuator) permits optimizing the LED output at selectwavelengths. This can be useful to compensate for any wavelengthsensitivity of the EPCS digital detector 150.

In an example where one or more of the light source elements 123comprise LEDs, the LSE controller 405 or the system controller 400 canbe configured to provide pulsed operation to extend the LED lifetime andreduce the need for heat dissipation, thereby eliminating the need forheat sinks and resulting in a much more compact EPCS light source 112.The pulse control system for the LEDs can include current and/orduration control to permit better matching the light available to theband pass filter transmission and detector sensitivity at the givenwavelength. For example, when a “white” LED is being used to provideseveral different measurement wavelengths, the digital detector exposuretime can remain consistent with the available light being controlled bythe LED driver. Pulsing the LEDs during the detector exposure time canalso permit low duty cycle overdrive of the LED to obtain higherintensity.

The focused configuration of the EPCS sub-system 100 (i.e., wherein thefocusing optical system 121 forms the focused EPCS light beam 116F)facilitates accurate optical alignment with little loss of light duringthe EPCS measurement of the CS substrate 10. The range of measurementangles relative to the normal of first coupling interface INT1 (seeFIGS. 22B and 22C) is related to the angle of total internal reflection.When the CS substrate 10 has an index gradient that generally decreasesfrom the top surface 12 into the body 11 of the CS substrate, the rangeof angles needed to probe the TM and TE mode lines (fringes) 163TM and163TE (see FIG. 3B) increases but is still within a limited range. Byoptimizing the light source and detector view angles (i.e., morespecifically, enlarging the range of included angles in the filtered andfocused EPCS light beam 116F and thus in the filtered and reflected EPCSlight beam 116R), the light collection efficiency is increased,resulting in better images of the mode spectrum 160 for the differentwavelengths used.

FIG. 22C is a close-up simplified view of the EPCS sub-system 100 in thevicinity of the EPCS coupling prism 42A and corresponding portions ofthe EPCS light source system 110 and EPCS detector system 140illustrating an example illumination configuration. In particular, aKohler configuration is employed wherein the output end 132 of the lightguide 130 is imaged through the EPCS coupling prism 42A by the focusingoptical system 121 onto an entrance pupil EP of the EPCS detector system140. In an example, the entrance pupil EP resides at the focusing lens142 of the EPCS detector system 140 as shown. This configuration ensuresthat the full radiance of the sequentially filtered EPCS light beam 116emitted from the output end 132 of the light guide 130 is preserved inthe EPCS detector system 140. It also ensures equal illumination of allangles through the EPCS coupling prism 42A, which results insubstantially even intensity of the TM and TE mode lines (fringes) 163TMand 163TE captured by the EPCS digital detector 150.

An alternative configuration has the output of multiple light sourceelements 123 (such as a 2d or 3d cluster) focused at the input end 131of the light guide 130 to facilitate efficiently coupling thesequentially filtered EPCS light beam 116 into the light guide. In anexample shown in FIG. 23, a diffuser 137 (such as limited-anglediffuser) can be employed at or near the input end 131 of the lightguide 130 to improve the light distribution of the sequentially filteredEPCS light beam 116 entering the light guide and simplify the combinerby eliminating the use of dichroic mirrors.

The measurement methods using the enhanced EPCS sub-system 100 arerelatively fast and are based on controlling the timing relationshipsbetween activation of the light source elements 123, the rotation(azimuthal) position of the filter wheel 530 of the optical filterapparatus 500 and the exposure time (image capture time) of the EPCSdigital detector 150. In an example configuration of enhanced EPCSsub-system 100 used in experiments, the motorized filter wheel 530 wascontrolled using a ThorLabs FW103H high-current BSC201 Controller having8-32 taps. This provided the optical filter apparatus 500 with a(stepped) filter switching speed of between about 55 milliseconds (ms)to 60 ms. In an example experimental configuration, the optical filterassemblies 600 had a diameter of dimensions up to 1″ with a 6.35 mmthickness. This filter switching speed is still slower than the read outtime of the EPCS digital detector 150, which in an example can read 100frames per second, so that the filter switching speed was the limitingfactor in the measurement speed of the example experimentalconfiguration.

An alternative to the fast changing (stepping) filter wheelconfiguration is a continuously rotating filter wheel 530. The fastchange configuration requires a high current drive system 540 to startand stop the filter wheel 530 with adequate precision. A drive system540 configured to provide constant rotation of the filter wheel 530 usesrelatively little ongoing current to keep the filter wheel spinningwhile inertia from the mass of the filter wheel and optical filterassemblies 600 keep the motion sufficiently constant so that a simpleencoder, or simpler reference index sensor(s) can be used to indicateposition and even provide a trigger to the EPCS digital detector 150.The trigger can be used to activate the illumination from the lightsource elements 123 if they are not on continuously. In one example, theexposure time occurs within the duration when the majority (and in onfurther example, a maximum amount) of the measurement light passesthrough the given optical filter assembly 600. In another example, theexposure time occurs only when there is light passing through a givenoptical filter assembly 600 or when there is a minimum amount of lightpassing through a given optical filter assembly (e.g., more than 10% ofthe maximum amount).

The design of the support member 510 that forms the filter wheel 530 caninclude relatively large opaque regions between adjacent optical filterassemblies 600. This can allow the opaque regions to act like focalplane shutters and maximize the exposure duration to the full dimensionsof the given optical filter assembly 600 across the given mode spectrumimage. The exposure can start while the light is blocked by the opaqueregion, i.e., before the optical filter apparatus 500 reaches the lightsource axis AS and the light path of the light. The exposure continuesas the optical filter assembly 600 enters and crosses the light sourceaxis AS and then moves away. The exposure stops when the optical filterassembly completely exits the light path of the light and the nextopaque region finally reaches the light source axis.

FIGS. 25A and 25B are a close-up views of a portion of an example EPCSdetector system 140 illustrating two exemplary configurations of theenhanced EPCS sub-system 100 disclosed herein. The examples of the EPCSdetector system 140 employ multiple EPCS digital detectors 150, with thethree example EPCS digital detectors denoted 150 a, 150 b and 150 c,which are each operably connected to the system controller 400. Thethree example EPCS digital detectors 150 a, 150 b and 150 c arespatially separated using beam splitters 180, which in the example ofFIG. 25A can be conventional beam splitting elements. In one example,the EPCS digital detectors 150 a, 150 b and 150 c are used to detectrespective wavelengths λ_(a), λ_(b) and λ_(c). This can be accomplishedby placing respective narrow-band optical filters 144 a, 144 b and 144 cin front of each of the EPCS digital detectors 150 a, 150 b and 150 c.This configuration allows for simultaneous detection of mode spectrumimages and obviates the need for the optical filter apparatus 500 andits high-speed filter wheel configuration, but requires multiple EPCSdigital detectors 150 and data synchronization to handle simultaneousmode spectrum measurements. The relative axial positions of the EPCSdigital detectors 150 a, 150 b and 150 c along the respective opticalpaths can be set to compensate for any focusing differences due to thedifferent wavelengths of light employed. Likewise, additional focusinglenses 142 a, 142 b and 142 c can be employed to obtain proper focus atthe respective EPCS digital detectors 150 a, 150 b and 150 c.

In the configuration shown in FIG. 25B, the beam splitters arewavelength-selective elements 125 such as dichroic mirrors, so that theselect wavelength is directed to the corresponding EPCS digitaldetector. This obviates the need for individual narrow-band opticalfilters in front of the EPCS digital detectors 150.

FIG. 25C is similar to FIG. 25A except that each single optical filteris replaced by an optical filter apparatus 500 that includes multipleoptical filters arranged on a filter wheel 530 as described above.

The cost of using the light source system configuration employing asingle optical filter apparatus 500 having a high-speed filter wheel 530as shown in FIG. 23 could exceed that of using multiple EPCS digitaldetectors 150 as shown in FIGS. 25A and 25B so that in some embodimentswhere cost is a factor, the use of multiple EPCS digital detectors maybe preferred. The use of multiple EPCS digital detectors 150 has theadvantage that the detectors need not be operated at a high frame ratefor overall system speed since the speed comes from the simultaneousacquisition of the mode spectrum images using the multiple EPCS digitaldetectors 150. In this case, the exposure time drives the acquisitiontime, with the exposure time driven mainly by the intensity of the lightsource elements 123. The use of relatively high-power light sourceelements 123 can be used to drive down the exposure time.

Processing mode spectra 160 captured at different wavelengths allows fora more accurate analysis of the stress-related properties of the CSsubstrate 10. In some cases, the TM mode lines 163TM of a given modespectrum 160 taken at one wavelength are sharper (i.e., higher contrast)than the TE mode lines 163TE and vice versa. So, use of multiple modespectra 160 captured at different wavelengths allows for the best(highest contrast) TM and TE modes lines to be analyzed. A high contrastmode spectrum 160 allows for the positions of the TM and TE mode lines163TM and 163TE to be accurately determined. Further, the positions ofTM and TE mode lines 163TM and 163TE can be interpolated through pointsover the range of measurement wavelengths to better determine the truepositions of both real and virtual mode lines to extend the analysis.

The use of a remote EPCS light source 112 external to the main housingof the hybrid system 20 preserves space within the hybrid system,removes a heat source and provides access to service the components ofthe light source.

Enhanced LSP Sub-System

FIG. 26 is similar to FIG. 4A and illustrates an example of an enhancedLSP sub-system 200. The LSP light source system 210 of the enhanced LSPsub-system 200 now includes the following components operably disposedin order along the third axis A3 between the LSP light source 212 andthe first focusing lens: a shutter system 280, a rotating half-waveplate 234RH, and a fixed polarizer (with a fixed polarization direction)234F. The shutter system 280 can comprise for example a rotating shutterdriven by a drive motor. In an example, the LSP light source 212comprises a relatively high-power laser diode 213 with a light output(LSP light beam 216) centered at a select wavelength, such as 405 nm. Invarious examples, the laser diode 213 has an output power of at least 1milliwatt (mW) or at least 10 mW or at least 20 mW or at least 30 mW orat least 40 mW or at least 50 mW.

The optical compensator 230 now includes a spectrometer 260 operablydisposed along a spectrometer axis AS defined by the polarizing beamsplitter (PBS) 232. The optical compensator 230 also includes a fixedhalf-wave plate 234H, and a variable polarizer 234V arranged along thethird axis A3 and downstream of the PBS 232. The variable polarizer 234Vis driven by a polarization controller 237. A movable focusing lens 236resides downstream of the optical compensator 230. In an example, themovable focusing lens 236 is moved by a linear motor 272 and ismechanically attached thereto by a lens mount 270. In an example, thelens mount 270 can comprise a lens tube that is axially movable(slidable) within a support tube (not shown). In an example, the linearmotor 272 comprises a linear actuator configured to provide preciselinear movements. In an example, the variable polarizer 234V comprises aliquid crystal variable retarder (LCVR). In an example, a temperaturecontroller 235 is in operable communication with the variable polarizer234V to provide temperature stabilization to avoid changes inpolarization with temperature.

Use of a relatively high-power laser diode in the LSP light source 212facilitates making stress-related measurements for CS substrates 10 madeof a glass material, which has an amorphous structure that does notscatter as much as the crystalline structure of a glass ceramicmaterial. The PBS 232 is optimized for performance at the selectwavelength (e.g., 405 nm), which optimizes the amount of light directedtowards the CS substrate 10 under test. The combination of the half-waveplate 234H and the PBS 232 allows for automatic light intensity controlat the CS substrate 10, making it possible to alternate betweenmeasuring glass and glass-ceramic CS substrates.

The spectrometer 260 is disposed to receive a portion of the LSP lightbeam 216 and spectrally process the LSP light beam. The spectrometer 260serves two main functions. A first function is to monitor in real timethe wavelength of the LSP light beam 216, thereby allowing forwavelength calibration. A second function is to monitor changes in theoutput power of the laser diode. Thus, the term “spectrally process” caninclude performing at least one or both of the aforementioned first andsecond functions.

In an example, the temperature controller 235 allows the LCVR of thevariable polarizer 234V to be operated at a slightly elevatedtemperature relative to an ambient temperature such as room temperate(e.g., between about 35° C. and 40° C.), thereby reducing the effect ofroom temperature fluctuations on polarization and improving measurementstability and cycle time. In an example, the spectrometer 260 can be acommercially available spectrometer or can be one fabricated fromstandard components, such as diffraction gratings, a series ofnarrow-band notched filters, etc., as is known in the art.

The high-power laser diode 213 having about 50 mW of output power may beabove the required power needed to obtain enough scattering intensityfor certain types of CS substrates 10. However, the exact amount of theLSP light beam 216 entering the CS substrate 10 can be preciselycontrolled with the rotating half-wave plate 234RH in conjunction withthe PBS 232.

FIG. 27A is a schematic diagram that shows an example of how to performintensity control of the laser diode 213. A linearly polarized LSP lightbeam 216 from the laser diode 213 passes through the rotating half-waveplate 234RH and is incident upon the PBS 232, which splits the LSP lightbeam into two beams directed to and detected by the photodetectors PD1and PD2, which in turn are operably connected to the system controller400. Note that in practice portions of the LSP light beam 216 can bedirected to photodetectors PD1 and PD2 incorporated into the enhancedLSP sub-system 200 using additional beam splitters (not shown). Forexample, one beam splitter can be placed along the axis AS upstream ofthe spectrometer 260 while another beam splitter can be placed justdownstream of the PBS 232.

FIG. 27B is a plot of the normalized optical power OP versus the angle θ(°) of the rotating half-wave plate 234RH for the transmitted (T) andreflected (R) portions of the LSP light beam 216 formed by the PBS 232for an example experimental configuration using a laser diode 213. It isseen that the measured powers at the photodetectors PD1 and PD2 varywhen the rotating half-wave plate 234RH is rotated. The mirror imagesignature of the T and R plots is expected, as the rotating half-waveplate effectively rotates the polarization of the light prior toentering the PBS 232. The amount of vertically and horizontallypolarized intensities depends on the polarization orientation of LSPlight beam 216 from the laser diode.

With reference again to FIG. 26, the movable focusing lens 236 providesa stable solution for focusing the LSP light beam 216 onto the CSsubstrate 10 being analyzed with micrometer resolution. In addition,computer-control (via system controller 400) ensures repeatabilityacross different hybrid systems 20, as the position of the focusing lens236 can be made the same.

The absolute position of the focusing lens 236 can affect CT (centraltension) measurements of the CS substrate 10. FIG. 28 is a plot of CT(MPa) versus focusing lens position LP (mm) (measured relative to areference position) based on measurements performed on an example CSsubstrate 10. The measurements show about 5 MPa variation in themeasured CT across a 2 mm range of motion for the focusing lens 236. Theproper placement of the focusing lens 236 ensures accurate andrepeatable stress-related measurements.

As noted above, an example variable polarizer 234V comprises a LCVRdriven by the polarization controller 237. During a typical measurementusing the LSP sub-system 200, the LCVR is excited by a series ofvoltages provided by the polarization controller 237, with a delay ofabout 200-milliseconds between voltages. This time delay allows fordevice response time and image capture and accounts for most of themeasurement cycle time.

Although the LCVR operates well at room temperature, its response timecan improve substantially (e.g., by up to 3-fold) with increasingtemperature, which reduces the response time by reducing the viscosityof the liquid crystal material in the LCVR. In an example, the LCVR isexcited with an amplitude-modulated (AM) signal and its response time isdetermined using an oscilloscope. A decreasing trend of the LCVRsettling time with temperature supports the feasibility of measurementcycle time reduction. In addition, as noted above, operating at anelevated temperature relative to the room (ambient) temperature(e.g., >30° C.) can reduce or eliminate the effect of temperaturefluctuations on polarization, thereby resulting in higher stability andrepeatability across multiple stand-alone LSP sub-systems 200.

An example enhancement to the LSP sub-system 200 includes a calibrationprocess that includes camera angle calibration and camera tiltcompensation. FIG. 29 is similar to FIG. 11B but with different labelsfor the pertinent parameters. The camera angle is denoted β and ismeasured relative to a horizontal axis while t_(r) is the real CSsubstrate thickness (which can be measured with a caliper, for example)and t_(i) is the perceived CS substrate thickness in the image plane(i.e., at the digital detector 246). The camera viewing plane is denotedCVP and the viewing direction is denoted z (z-axis). The camera angle βis related to the parameters t_(i) and t_(r) via the relationship Cosβ=t_(i)/t_(r).

A camera tilt angle θ measures an amount of camera rotation around thez-axis. A deviation in the camera tilt angle θ can change the way theimage plane thickness is calculated. As shown in FIG. 29, thecalculation for the CS substrate thickness t_(r) is no longer thevertical distance between the entrance and exit points, but requiresmore calculations using trigonometry to account for the deviation angleθ.

An aspect of the disclosure includes an enhanced beam centering methodthat involves two main steps, namely an improved beam-center step and animproved center-point detection step for an X-shaped LSP image 248(including one of the processed images as described above) as formed bythe detected scattered LSP light beam 216S. (see FIG. 10A).

1) Enhanced Beam Centering Method

The improved beam-centering step includes two sub-steps. The firstsub-step finds the beam center along the beam path by modeling thehorizontal image intensity profiles (I) at each depth of the substrateusing the model intensity profile (I_(M)) given by

${{I_{M}(p)} = {{ae^{{- 2}{(\frac{p - b}{c})}^{2}}} + {dp} + f}},$

where the first term models the beam intensity profile as a Gaussianfunction with a, b and c being peak intensity, center and radius of aGaussian, respectively, while the last two terms model backgroundintensity profile (e.g. ambient light, camera dark counts, non-uniformcamera response) with d and f being a slope and constant level ofbackground intensity, respectively. p is the value of horizontal pixelin the image. The beam center is then found as the center of theGaussian beam from the best fit of I_(M) to I.

FIG. 30A is a plot of the intensity I(p) versus the pixel number p(x)for a select depth into the CS substrate 10 along the beam path in thex-direction. The fit estimates the center of one of the scattered LSPlight beams 216S (i.e., one of the line images in the X-shaped LSP image248; see FIG. 4D or FIG. 30C, the latter being introduced below), asindicated by the large black dot denoted CNTR. Once a list of peakcenters at each depth along the beam path has been collected, in asecond sub-step a line fit is applied through all the estimated peakcenters, as shown in the plot of FIG. 30B, which shows the peak centersfit in terms of the pixels located along the x and y directions, whichare respectively denoted p(x) and p(y). The results of the method werecompared to actual beam images and showed the method located the centerof the scattered beam with high accuracy.

2) Enhanced Center Point Detection

The enhance center point detection method makes use of the Gaussianfitting method described above to track the beam centers. FIG. 30C is aschematic diagram similar to FIG. 10C that shows an LSP image 248(intensity contour) with two superimposed fit lines FL1 and FL2 runningthrough the center of the two line-image sections, denoted 248-1 and248-2. The intersection INT of the two fitted lines FL1 and FL2represents the center point of LSP image 248.

3) Enhanced Entrance Point Method

A parameter of interest for the LSP image 248 is called the entrancepoint and is denoted as ENP in FIG. 30C. Determining the entrance pointmakes use of the fitted centerlines FL1 and FL2 established by theabove-described Gaussian fitting method that finds the beam centers as afunction of the beam intensity. The entrance point ENP is then chosen asthe half-max value on the edge intensity profile along the centerlinefit for the LSP image 248. FIG. 30D is a plot of the LSP image intensityI(p) vs. pixel position p along the fitted line FL2 and in the vicinityof the entrance point ENP (see FIG. 30C). The plot of FIG. 30D shows anexample edge intensity profile and identifies the maximum intensityI_(MAX), the minimum intensity I_(MIN) that represents a background or azero intensity value (e.g., by shifting the intensity curve), and thehalf-maximum intensity I_(1/2), which resides midway between I_(MAX) andI_(MIN) and defines the position (pixel location) of the entrance pointENP, which in the example plot is about at pixel 32. The pixel 32 can becorrelated with a physical position on the CS substrate 10 to obtain theentrance point ENP in the coordinate system of the CS substrate.

It will be apparent to those skilled in the art that variousmodifications to the preferred embodiments of the disclosure asdescribed herein can be made without departing from the spirit or scopeof the disclosure as defined in the appended claims. Thus, thedisclosure covers the modifications and variations provided they comewithin the scope of the appended claims and the equivalents thereto.

What is claimed is:
 1. An evanescent prism coupling spectroscopy (EPCS)system for characterizing stress in a chemically strengthened (CS)substrate having a surface and a near-surface waveguide, comprising: a)an EPCS light source system comprising: iv) an EPCS light source thatemits a multiwavelength EPCS light beam; v) an optical filter assemblyconfigured to sequentially filter the multiwavelength EPCS light beam toform a sequence of filtered EPCS light beams having differentwavelengths; vi) a light guide assembly that transfers the sequence offiltered EPCS light beams as guided light to a focusing optical systemarranged to receive the transferred filtered EPCS light beams and formtherefrom a sequence of filtered and focused EPCS light beams; b) anEPCS coupling prism that forms an EPCS coupling surface with the surfaceof the CS substrate and that receives and couples the sequence offiltered and focused EPCS light beams into and out of the near-surfacewaveguide at the EPCS coupling surface to form a sequence of filteredand reflected EPCS light beams that respectively comprise mode spectraof the near-surface waveguide for the corresponding filtered andreflected EPCS light beam; and c) an EPCS detector system comprising: i)a switchable polarization filter operably connected to a polarizationcontroller to sequentially perform transverse magnetic (TM) andtransverse electric (TE) polarization filtering of the sequence offiltered and reflected EPCS light beams to form TM and TE filtered andreflected EPCS light beams respectively comprising TM and TE modespectra of the near-surface waveguide; and ii) an EPCS digital detectorconfigured to sequentially detect the sequence of TM and TE filtered andreflected EPCS light beams to sequentially capture TM and TE images ofthe respective TM and TE mode spectra of the near-surface waveguide atthe different filter wavelengths.
 2. The EPCS system according to claim1, wherein the optical filter assembly comprises an optical filterwheel.
 3. The EPCS system according to claim 1, wherein the light guideassembly comprises a light guide with an output end, the EPCS detectorsystem comprises an entrance pupil, and wherein the output end of thelight guide is imaged onto the entrance pupil by the focusing opticalsystem.
 4. A hybrid system for characterizing stress in a chemicallystrengthened (CS) substrate having a top surface and a near-surfacewaveguide, comprising: The EPCS system according to claim 1; a scatteredlight polarimetry (LSP) sub-system comprising a LSP light source system,an optical compensator and a LSP detector system in opticalcommunication with the optical compensator through an LSP coupling prismhaving a LSP coupling surface; and a coupling prism assembly comprisinga prism support frame configured to operably support the EPCS and LSPcoupling prisms so that the EPCS and LSP coupling surfaces residessubstantially in a common plane; and a support plenum having a surfaceand a measurement aperture, the support plenum configured to support theCS substrate at a measurement plane at the measurement aperture, and tooperably support the coupling prism assembly at the measurement apertureso that the EPCS and LSP coupling surfaces reside substantially at themeasurement plane.
 5. An evanescent prism coupling spectroscopy (EPCS)system for characterizing stress in a chemically strengthened (CS)substrate having a surface and a near-surface waveguide, comprising: a)an EPCS light source system comprising: iv) an EPCS light source thatemits a multiwavelength EPCS light beam; v) an optical filter assemblyconfigured to sequentially filter the multiwavelength EPCS light beam toform a sequence of filtered EPCS light beams having different filterwavelengths; vi) a light guide assembly that transfers the sequence offiltered EPCS light beams as guided light to a focusing optical systemarranged to receive the transferred filtered EPCS light beams and formtherefrom a sequence of filtered and focused EPCS light beams; b) anEPCS coupling prism that forms a EPCS coupling surface with the surfaceof the CS substrate and that receives and couples the focusedsequentially filtered EPCS light beam out of the near-surface waveguideat the EPCS coupling surface to form a reflected and sequentiallyfiltered EPCS light beam that comprises at least first and second modespectra of the near-surface waveguide for the at least first and secondfilter wavelengths; and c) an EPCS detector system comprising: i) atleast one switchable polarization filter configured to sequentiallyperform transverse magnetic (TM) and transverse electric (TE)polarization filtering of the reflected and sequentially filtered EPCSlight beam to form at least first and second TM and TE reflected andsequentially filtered EPCS light beams respectively comprising first andsecond TM and TE mode spectra of the near-surface waveguide at the atleast first and second wavelengths, respectively; and ii) at least firstand second EPCS digital detectors configured to respectively detect theat least first and second TM and TE reflected and sequentially filteredEPCS light beams to capture respective at least first and second TM andTE images of the first and TM and TE mode spectra of the near-surfacewaveguide.
 6. The EPCS system according to claim 5, wherein the at leastfirst and second EPCS digital detectors reside along respective at leastfirst and second detector axes, and wherein the at least one switchablepolarization filter comprises at least first and second switchablepolarization filters respectively arranged along the at least first andsecond detector axes and upstream of the corresponding one of the atleast first and second EPCS digital detectors.
 7. The EPCS systemaccording to claim 5, wherein the CS substrate comprises a glassmaterial, a glass-ceramic material or a crystalline material, andwherein the near-surface waveguide of the CS substrate is defined by anear-surface spike region and a deep region.
 8. The EPCS systemaccording to claim 5 wherein the light guide assembly comprises a lightguide with an output end, the EPCS detector system comprises an entrancepupil, and wherein the output end of the light guide is imaged onto theentrance pupil.
 9. A system for characterizing stress in a chemicallystrengthened (CS) substrate having a top surface and a near-surfacewaveguide, comprising: The EPCS system according to claim 5; a scatteredlight polarimetry (LSP) sub-system comprising a LSP light source system,an optical compensator and a LSP detector system in opticalcommunication with the optical compensator through an LSP coupling prismhaving a LSP coupling surface; a coupling prism assembly comprising aprism support frame configured to operably support the EPCS and LSPcoupling prisms so that the EPCS and LSP coupling surfaces residessubstantially in a common plane; and a support plenum having a surfaceand a measurement aperture, the support plenum configured to support theCS substrate at a measurement plane at the measurement aperture, and tooperably support the coupling prism assembly at the measurement apertureso that the EPCS and LSP coupling surfaces reside substantially at themeasurement plane.
 10. A light scattering polarimetry system forcharacterizing stress in a chemically strengthened (CS) substrate havinga body, a surface and a near-surface waveguide formed within the body,comprising: a) a LSP light source system comprising in order along afirst system axis: i) a laser diode that emits a LSP light beam havingat least 1 microwatt of power and centered on a wavelength of 405nanometers; ii) a shutter system arranged to periodically block the LSPlight beam; iii) a rotatable half-wave plate; iv) a first fixedpolarizer; v) a first focusing lens; vi) a light diffuser; vii) a secondfocusing lens b) an optical compensator arranged downstream of the LPSlight source and configured to impart to the LSP light beam atime-varying polarization, the optical compensator comprising in orderalong the system axis: i) a polarizing beam splitter arranged to receivethe LSP light beam from the LSP light source and transmit a firstportion of the LSP light beam along the first system axis and to directa second portion of the LSP light beam along a spectrometer axis; ii) aspectrometer arranged along the spectrometer axis and arranged toreceive and spectrally process the second portion of the LSP light beam;iii) a second fixed polarizer; iv) a variable polarizer that imparts thetime-varying polarization to the LSP light beam to form a time-varyingpolarized LSP light beam; c) an axially movable focusing lens arrangeddownstream of the optical compensator and configured to receive andfocus the time-varying polarized LSP light beam form a focusedtime-varying polarized LSP light beam; d) an LSP coupling prisminterfaced with surface of the CS substrate to form a LSP couplinginterface, wherein the focused time-varying polarized LSP light beam isfocused at the LSP coupling interface to generate scattered light fromstress-induced features within the body of the CS substrate; e) a LSPdetector system arranged downstream of the LSP coupling prism andarranged to receive the scattered light, the LSP detector systemcomprising: i) a LSP digital detector; and ii) a collection opticalsystem that collects and directs the scattered light to the LSP digitaldetector to form an LSP image at the digital detector.
 11. The LSPsystem according to claim 10, wherein the variable polarizer comprises aliquid crystal variable retarder (LCVR) operably connected to apolarization controller.
 12. The LSP system according to claim 10,wherein the LCVR is in operable communication with a temperaturecontroller that maintains the LCVR within a select temperature range.13. The LSP system according to claim 12, wherein the select temperaturerange is between 35° C. and 40° C.
 14. The LSP system according to claim10, wherein the axial movable focusing lens comprises a lens elementsupported by a lens support and wherein the lens support is mechanicallyattached to a linear motor.
 15. The LSP system according to claim 10,wherein LSP light beam has at least 10 microwatts of power.
 16. The LSPsystem according to claim 10, wherein LSP light beam has at least 50microwatts of power.
 17. The LSP system according to claim 10, whereinthe LSP system is configured to perform the following steps: a)estimating a beam center (CNTR) of the time-varying polarized lightbeam, where the time-varying polarized light beam follows a beam paththrough the body of the CS substrate, by: i) performing a tiltedGaussian fit to the scattered light for select depths into the body ofthe CS substrate along the beam path to define a first set of beamcenters; and ii) fitting a first line through the first set of beamcenters to define a first fitted line; b) estimating a center point ofthe time-varying polarized light beam by fitting a second line through asecond set of beam centers to define a second fitted line, andidentifying the center point where the first and second fitted linescross; and c) Identifying an edge intensity profile of the LSP imagealong one of the first and second fitted lines where the edge intensitytransitions from a maximum value I_(MAX) to a minimum value I_(MIN)representative of a background intensity value; and determining ahalf-maximum intensity value I_(1/2) midway between the maximum andminimum intensity values I_(MAX) and I_(MIN) and defining the entrancepoint to be at the half-maximum intensity value I_(1/2).
 18. A systemfor characterizing stress in a chemically strengthened (CS) substratehaving a top surface and a near-surface waveguide, comprising: the LSPsystem according to claim 10; an evanescent prism coupling spectroscopy(EPCS) sub-system comprising a EPCS light source system and a EPCSdetector system in optical communication through an EPCS coupling prismhaving a EPCS coupling surface; a coupling prism assembly comprising aprism support frame configured to operably support the EPCS and LSPcoupling prisms so that the EPCS and LSP coupling surfaces residessubstantially in a common plane; and a support plenum having a surfaceand a measurement aperture, the support plenum configured to support theCS substrate at a measurement plane at the measurement aperture, and tooperably support the coupling prism assembly at the measurement apertureso that the EPCS and LSP coupling surfaces reside substantially at themeasurement plane.